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A bathtub that initially holds 50 gallons of water starts

Explorations in College Algebra | 5th Edition | ISBN: 9780470466445 | Authors: Linda Almgren Kime ISBN: 9780470466445 178

Solution for problem 6 Chapter 2

Explorations in College Algebra | 5th Edition

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Explorations in College Algebra | 5th Edition | ISBN: 9780470466445 | Authors: Linda Almgren Kime

Explorations in College Algebra | 5th Edition

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Problem 6

A bathtub that initially holds 50 gallons of water starts draining at 10 gallons per minute. a. Construct a function W(t) for the volume of water (in gallons) in the tub after t minutes. b. Graph the function and label the axes. Evaluate W(0) and W(5) and describe what they represent in this context. c. How would the original function and its graph change if the initial volume were 60 gallons? Call the new function U(t). d. How would the original function and graph change if the drain rate were 12 gallons per minute? Call the new function V(t). e. Add the graphs of U(t) and V(t) to the original graph of W(t)

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CH. 23 Animal Origins and Diversity 23.1: Distinct Body Plants Evolved among the Animals Diploblastic Animals: Two cell layers w/ non -living layer between (retains ancestral condition) Triploblastic Animals: Three cell layers (Synapomorphy) à bilaterians Gastrulation: process of development, a hollow ball of cells indents forming cavity (blastopore) Bilaterians: (triploblastic animals) clade which has similarity of bilateral symmetry Protostomes: blastopore develops into mouth, anus forms later Deuterostomes: blastopore develops into anus, mouth forms later Body Plan: general structure of animal/arrangement of organ systems & integrated functioning Four key features impact interaction w/ environment: - Symmetry of body - Body cavity structure - Body segmentation - Existence/location of external appendages (sensing, feeding, locomotion, mating) Symmetry: can be divided along at least one plane into similar halves Radial: body parts arranged around central axis; some sessile Bilateral: distinct front end that rest of body follows; divides into mirror -image (Anterior: front, Posterior: rear, Dorsal: top, Ventral: bottom) Cephalization: concentration of sensory organs and nervous tissues at anterior end/head - Often w/ bilateral symmetry - Evolutionarily favored b/c anterior end usually encounters environment first Body Cavity: divides animals w/ three embryonic layers into three types Acoelomate: Lacks enclosed fluid-filled body cavity - Space between gut (derived from endoderm) and body wall (mesoderm) is filled w/ c ells called mesenchyme - Move by beating cilia Pseudocoelomate: Body cavity is a pseudocoel, fluid-filled space w/ suspended internal organs - Pseudocoel enclosed by muscles (mesoderm) only on outside - Lacks inner layer of mesoderm surrounding internal organs Coelomate: Body cavity is a coelom that develops within mesoderm - Layer of muscular tissue peritoneum lines coelom/surrounds internal organs - Enclosed on inside/outside by mesoderm 23.4: Anthropods are Diverse and Abundant Animals Arachnids: Spiders, scorpions, harvestmen, mites, ticks - Simple life cycle - Some are parasites Madibulates: (myriapods, crustaceans, hexapods) - Mandibles used for chewing/biting - Head w/ sensory antennae Myriapods: Centi/millipedes - Segmented trunks w/ many pairs of legs - Centipedes have one pair per segment; Millipedes have two pairs per segment Crustaceans: Shrimp, lobsters, crayfish, crabs - Appendages on diff parts of body have specialized functions - Three regions of body: head, thorax, abdomen Hexapods: (insects) - Jointed appendages - Exoskeleton - Segmented body à Myriapoda Subphylum Class(es) Chelicerata Arachnida (Spiders, scorpions, mites, ticks) Hexapoda Insecta (most diverse/numerous) Entognatha (dipluran, collembolan, protura, soil insects) Crustacea (Isopods) Myriapoda (Centi/millipedes) Insects vs. Arachnids Insects: (Hexapoda) three body divisions, three pairs of legs Arachnids: two body divisions, four pairs of legs Regions of Insect: Hexapoda (6 legs) 1. Head: sensory perception, food gathering; external mouthpart s 2. Thorax: locomotion; 3 pairs of legs attached, sometimes 2 pairs of wings 3. Abdomen: Contains visceral organs - Spiracles, external openings allowing for gas exchange system of air sacs/tracheae to extend from - Began to diversify when land plants appeared Body Parts: 1. Apterygota: No wings (Collembola, Thysanura) 2. Paleoptera: Old wings don’t fold together (Odonata, Ephemeroptera) 3. Exopterygota: Wings develop externally (Orthopteroids, Hemipteroids) 4. Endopterygota: Wings develop inside pupil stage, Holometabolous/Co mplete metamorphasis (Hymenoptera, Coleoptera, Neuroptera, Lepidoptera, Siphonaptera, Diptera) Pterygote: 2 pairs of wings, but pairs may have been lost in some groups - First flying animals Neopterans: insects that tuck wings out of way when landing - Some have incomplete metamorphosis, some have complete - Highly specialized social behaviors Distinguishing Characteristics of Insects: 1. Feeding Strategies: chewing vs. piercing/sucking 2. Life Cycles: metamorphosis 3. Evolvability Metamorphosis: substantial morphological changes between developmental stages - Ametabolous: without metamorphosis, molts to adult size only changing size - Paurometabolous: gradual development from egg à nymph à adult - Incomplete: In aquatic habitats, change from egg à naiad à adult - Holometabolous: Dramatic changes from egg à larvae à pupil (rearrangement of entire morphology of organism) à adult o Larvae often adapted for feeding/growing; adults specialized for reproduction/dispersal - Homologous genes control development of insect wings/crustacean ap pendages 23.5: Deuterostomes Include Echinoderms, Hemichordates, and Chordates Deuterostomes: triploblastic and coelomate - Have internal skeletons - Includes many large animals (Humans) - Complex behaviors develop in some groups (greater memory development) Echinoderms: Sea stars, sea urchins; Nearly all marine - Ciliated larvae have bilateral symmetry, but adults have radial symmetry/lack head - Oral side (mouth) and aboral side (anus) - Most used to be sessile and attached to substrate by stalk; Now are mostly moti le - Water vascular system : network of water-filled canals leading to extensions, tube feet - Tube feet allow for gas exchange, locomotion, feeding; modified to capture prey Hemichordates: Acorn worms, pterobranchs - Three body parts: proboscis, collar, trunk - Ciliated larvae have bilateral symmetry, but adults have radial symmetry/lack head - Acorn worms: capture prey with proboscis - Pterobrancs: live in tubes secreted by proboscis Chordates: Lancelets, Tunicates, Vertebrates - Evolutionary relationships between clade s are most evident in early developmental stages - Derived structures: o Dorsal hollow nerve cord o Tail extending past anus o Notochord: Core of large cells w/ fluid -filled vacuoles, rigid but flexible; protects nerve cord o Pharyngeal slits: Ancestral pharyngeal s lits often lost as adults; aids gas exchange - Lancelets: Notochord persists throughout life - Tunicates: Notocord lost during metamorphosis to the adult stage o Sessile adults; reproduce through asexual budding Vertebrates: - Jointed, dorsal vertebral column replaces notochord (backbone) - Evolved in oceans to radiate into marine, freshwater, terrestrial, aerial environments Key Features: Allowed them to become large, active predators 1. Anterior skull w/ large brain 2. Rigid internal skeleton supported by vertebral col umn: support for muscular system 3. Internal organs suspended in coelom 4. Well-developed circulatory system w/ ventral heart: Oxygen transportation Living Vertebrates: Jawless Fish: Hagfishes: Sister group of all other vertebrates - 3 small hearts, partial cranium, no jaws, skeleton mainly made of cartilage, blind - Gene sequences of miRNA suggest they lost many vertebrate features o Results: Hagfishes share more recent common ancestor with lampreys than lampreys do w/ other vertebrates o Form a monophyletic group, both vertebrates Lampreys: - Complete skill and cartilaginous vertebrae - Undergo complete metamorphosis from ammocoetes - Mostly parasitic adults; some are nonfeeding Gnathostomes: Jaw fishes; Jaws/teeth evolved from skeletal gill arches - One lineage à Bony vertebrates à Ray-finned fishes vs. Lobe-limbed vertebrates Chondrichthyans: Sharks, rays, chimaeras - Skeleton of pliable cartilage/leathery skin 23.6: Life on Land Contributed to Vertebrate Diversification Gnathostomes à Bony Vertebrates Bony-Vertebrates: skeletons of calcified, rigid bone - Gas-filled sacs extended from digestive tract to supplement gas exchange by gills à Swim bladders/lungs Ray-Finned Fishes: Body covered with scales; Lobe-Limbed Vertebrates: Paired gills open into chamber pelvic/pectoral fins became more muscular - Lungfishes: lungs and gills - Tetrapods: four-legged vertebrates; limbs adapted for movement on land Tetrapods: Amphibians: moist habitats (frogs, toads, Amniotes: colonize drier habitats salamanders) - Adaptations: amniote eggs, tough skin - Some entirely aquatic, some live on dry w/ scales to prevent drying, excretory land and must return to water to lay eggs organs allow excretion of urine and larvae develop in water - Amniote eggs: store food for embryo in - Anurans: (frogs/toads) is largest group; form of yolk, extraembryonic all have pelvic region modified for membranes prevent desiccation hopping/kicking in water o Modified allowing embryo to - Salamanders: completely aquatic grow inside of mother’s body species have evolved several times o In mammals, shell was lost and through neoteny (retention of juvenile extraembryonic membranes characteristics such as gills); internal expand fertilization - Amniotes à reptiles à mammals Sex Determination: (in turtles) - Temperature can affect it by turning on/off certain enzymes (Ex: turtles that lay eggs in higher temperatures results in greater percentage of female offspring) - As egg develops further increasing in size, metabolic rate would increase, increasing body heat given off by eggs; sex determination occurs later when temperature has increased à increased female population - Increase in max nest temperature à increased number of metabolizing embryos Reptiles: Lepidosaurs: skin w/ horny scales reduce water loss, gas excha nge through lungs, three -chambered heart - Squamates: lizards, snakes and amphisbaenians o Most lizards are insectivores o Snakes are limbless squamates/carnivorous - Tuataras: resemble lizards; only 2 species survive Therapods: predatory dinosaurs that had many c haracteristics of birds… - Characteristics: o Bipedal o Backwards pelvis o Hollow bones o Many are homeothermic o Furcula (wishbone) (maintains same temperature o 3 Fingered feet/hands using metabolism) - Scales à feathers Mammals: coexisted with dinosaurs for million s of years - Extinction of non-avian dinosaurs à mammals diversified and grew larger - Highly differentiated teeth - Key Features: o Sweat glands o Mammary glands o Hair (insulation) o 4-chambered heart separates oxygenated blood from deoxygenated blood - Eggs fertilized internally within female’s body, embryos develop in uterus - Embryo contained in amniotic sac, connected to uterine wall by placenta which allows for nutrient/gas exchange and waste elimination - Prototherians: (duck-billed platypus, Therians: all other mammals echidnas) o Marsupials: carry/feed young in ventral o Lack placenta, lay eggs pouch; born early & crawl into pouch o Sprawling legs for further development o Eutherians: rodents, bats, moles and shrews; several lineages go to H2O Primates: evolved from lineage of small, arboreal, insectivorous eutherian; 2 clades… - Prosimians: (lemurs, lorises, galagos) - Anthropoids: (tarsiers, old/new world monkeys, apes) o New- arboreal, prehensile tails o Old- Some are arboreal/terrestrial, none of tails Hominid clade à humans - Human brains became larger as jaws became smaller (enabled communication) Bipedal Locomotion: evolved in arpidithecines (protohominids) - Frees forelimbs to manipulate objects - Elevates eyes, allowing it to see predator/prey - Energetically favored compared t o quadrupedal locomotion CH. 40 Behavior Behavior: Response to a stimulus -­‐‑ Response could be learned or fixed Environmental Change à Stimulus -­‐‑ Adjustments of behavior are often the most visible responses to environmental change -­‐‑ Ex: Many migratory animals change timing of migrations in response to climate change 40.1: Behavior is Controlled by the Nervous System but is Not Necessarily Deterministi c An animal’s nervous system activates/coordinates behaviors: Fixed Action Patterns: highly stereotyped animal behaviors that are expressed without prior learning; often resistant to modification by learning -­‐‑ Ex: begging behavior of gull chicks peck at re d dot on bills; spiders’ web spinning -­‐‑ Ex: The ultimate cause of what the male three -spined stickleback attacks other males entering his nesting territory is to increase their reproductive ability -­‐‑ Behaviors evolve: Natural selection favors the alleles that produce more adaptive behaviors than others o Many studies show that genes exert important effects on behavior o Ex: In Drosophila mutants for gene per altered circadian rhythms Biological Determinism: behaviors of animals are hardwired by genetics; individu al’s genes change neural properties in fixed ways that affect behavior -­‐‑ Behavior is more flexible than any other biological trait b/c learning modifies behavior -­‐‑ Epigenetic effects on behavior à lifelong influences; can be transmitted to next generation -­‐‑ Ex: Clams are inflexible in many of their responses to their environment 40.2: Behavior is Influenced by Development and Learning Learning: ability of individual to modify its behaviors as a consequence of individual experiences -­‐‑ Ex: Experiments with mice sh ow that they learn layout/hiding places of their environment, learning that helps them escape predation by screech owls. -­‐‑ Learning is taught through patterns of recognition, whereas fixed action pattern is not Behavioral Imprinting: type of learning that is taught; takes place within a narrow window of time early in postnatal life and after is inflexible -­‐‑ Can have lifelong consequences -­‐‑ Nutrition can impact efficacy of imprinting o Migratory locusts behave based on density/diet; those on less protein diet fle w faster o Hungry adult offspring of “low -caring” mothers wait longer than those of “high -caring” mothers to go to food and spend less time eating food -­‐‑ Examples o Geese hatchlings imprint on their “parents” establishing a strong attraction o Species-specific songs of Darwin’s male finches are learned within first month of life used to attract females -­‐‑ Particular brain regions required for this learning o Key regulatory genes in stress -response biochemical/hormonal pathways are tagged with epigenetic marks early on in life permanently altering their stress responses 40.3: Behavior is Integrated with the Rest of Function Ex: Pronghorn have the highest sustained speeds in running animals -­‐‑ Muscles use aerobic respiration and systems o Delivers O to muscles at higher rates 2 o Use O at 2igher rates to make ATP in muscle cells o Use ATP at higher rates to perform intense muscular work -­‐‑ Exceptionally large lungs/skeletal muscles, and muscle cells are tightly packed with mitochondria Escape behavior is dependent upon ATP synthesis -­‐‑ Aerobic ATP is slow, and resists fatigue -­‐‑ Anaerobic ATP is fast, but fatigue faster o Ex: Toads evolved enzymes for aerobic ATP production in legs; Frogs evolved them for anaerobic ATP production à leap away/fatigue faster Behaviors are dependent upon body s ize/growth -­‐‑ Ex: Tonal frequencies of insects’ songs vary based on body size; larger body à low frequency song -­‐‑ Ex: Young hyenas have teeth/jaws that aren’t developed enough to crush bones compared to adults 40.4: Moving through Space Presents Distinctive Ch allenges Navigation: act of moving toward a destination or along a course -­‐‑ Trail following o Pheromone: chemical compound/mixture emitted to outside environment that elicits specific behavioral responses from other members of the species o Can use pheromones t o attract members of opposite sex o Ex: Worker ants lay pheromone trail to guide others to a food source -­‐‑ Path Integration o Monitor length/compass direction of each segment and integrates the information about segment lengths/directions to determine where it i s relative to its nest Orientation: adopting a position or path of locomotion relative to an environmental cue (ie. sun) -­‐‑ Sun Compass: determine where N, S, E, W are by observing sun o Ex: Birds observe position of sun/time of day and adjusting their angle o f flight relative to the sun, using their circadian clock to know the time of day -­‐‑ Redundancy orientation mechanisms -­‐‑ Many insects determine compass direction by detecting patterns of polarized light in sky using specialized photoreceptors -­‐‑ Honey bee workers’ “Waggle Dance” o Communicates path to flowers using a dance based on measurements taken of distance/direction to the flowers § Measures distance by monitoring rate flying past landmarks § Measures direction by monitoring the angle of flight relative to the comp ass position of sun -­‐‑ Migration: move periodically from one location to another to remain for a substantial period of time and later return from o Ex: Young Loggerhead Sea turtles use Earth’s magnetic field, currents and temperature to orient themselves while traveling in closed circle across the Atlantic Ocean 40.5: Social Behavior is Widespread Society: group of individuals of a single species organized to some degree in a cooperative manner Social Behavior: behaviors of individuals that integrate them int o societies and the group behaviors of entire societies -­‐‑ Disadvantages o Grouping makes animals more visible o diseases spread more rapidly o resources are depleted more rapidly -­‐‑ Advantages of Equal Status o Enhanced awareness of environment (Ex: Goshawk’s success i n capturing pigeons decreases as number of pigeons in flock increase) o Discover preferred environments more efficiently -­‐‑ Advantages of Differing Statuses o Dominates: “wins” one-on-one behavioral contests with others; has greatest chance of mating with adult females in group o Enhanced awareness/discovery of preferred environments o Process of becoming dominant serves as a test of male’s strength, endurance, properties for success therefore females that mate with it ensure that their offspring are genetically well developed -­‐‑ Eusociality: social structure in which some members of social group are non -reproductive and assist reproduction of fertile members of group, usually mother o Mostly in insects o Exemplify Altruism: any characteristic of an individual that imposes a cost on that individual but aids another 40.6: Behavior Helps Structure Ecological Communities and Processes -­‐‑ Behavior helps maintain species due to reproductive isolation -­‐‑ Behaviorally partition space into territories o Territory: region occupied by individual that actively keeps others of same species out o Home Range: other individuals aren’t excluded o Provide familiarity (escape route, resources, etc) Cost-Benefit Approach: Assumes an animal has only a limited amount of time/energy and therefore cannot afford to engage in behaviors that cost more to perform than they bring benefits CH. 42 Population Ecology Ecology: The study of… -­‐‑ Ernest Haeckel (1869) came up with the word “ecology” o Oikos – house/home; “study of the household” -­‐‑ Vick’s definition: Economics of nature -­‐‑ Textbook: study of the relationships of organisms to their environment and one another The Economics of Nature: -­‐‑ Based on distribution/abundance of organisms o Individual organisms o Populations of organisms o Communities of organisms Ecology vs. Evolution Ecologists & Evolutionary Ecologists: look to understand/explain processes that determine the distribution, diversity, and abundance of organisms Ecologists: Evolutionary Ecologist s: Look for proximate answers for diversity, Look for ultimate answers for diversity, distribution, and abundance of organisms distribution, and abundance of organisms Ex: Why did the chicken cross the road A: To get away from a predator, find food, or A: migration pattern of the chicken went across find a mate the road, appendages carry it across the road, inclination to cross roads Ex: Colorado Potato Beetle is a pest in America (lg. population), not Mexico (sm. population) Proximate Causes: Ultimate Causes: -­‐‑ Pest Status: based on food availability, -­‐‑ Pest Status: evolved to process potatoes predation or endure cold conditions -­‐‑ Population Size: large amt of food -­‐‑ Population Size: evolved to live in increases population; potatoes less regions where natural enemies cannot defended survive Ecology: Changes in numbers of individuals o r Evolution: (Macroevolution) populations in ecosystems over a few Changes in traits in populations generations over many generations -­‐‑ Scope: Populations or individuals within -­‐‑ Scope: Traits within populations habitats -­‐‑ Timescale: Larger time frames -­‐‑ Timescale: Days/Years Ecology ßà Evolution Evolutionary change à changes in ecology à evolves abilities to survive differently Invasive Species: dispersal limitation Factors limiting Geographic Distribution -­‐‑ Dispersal -­‐‑ Behavior (Habitat selection) -­‐‑ Biotic factors (Other species, predation, competition, disease) -­‐‑ Abiotic factors (Chemical/physical) Density: # individuals per unit area or volume -­‐‑ Often impractical/impossible to count all individuals in a population -­‐‑ Sampling techniques used to estimate densities/ total population size Mark-Recapture Method: scientists capture, tag, and release random sample of individuals (m) in a population -­‐‑ Marked individuals are given time to mix back into the population -­‐‑ Scientists capture second sample of individuals (n) and n ote how many of them are marked (x) -­‐‑ Population size (N) is estimated by: N = mn / x because m / N = x / n -­‐‑ Ex: Scientist marked 180 dolphins and waited a few days to mix them. He observed 44 dolphins the second time, 7 of which were marked. m = 180 So N = (180) (44) / 7 = 1131 n = 44 x = 7 Density is the results of interplay between processes that add individuals to a population and those that remove individuals Immigration: influx of new individuals from other areas Emigration: movement of individuals o ut of a population Dispersion: pattern of spacing among individuals within the boundaries of a population (clumped, uniform, random) 42.1: Populations Are Patchy in Space and Dynamic over Time Populations: groups of individuals of the same species - Populations have properties that individuals lack - Must understand populations to understand larger ecological systems Population Density: number of individuals per unit area/volume - Measured if interested in causes/consequences of local abundance - Dynamic, changes over time Population Size: total number of individuals in a population - Population size = (Population Density) x (Area occupied by the population) Humans are interested in understanding species abundance: o To increase populations of species that provide resources/food o To decrease abundance of crop pests, pathogens, etc. - Varies on spatial scales: Geographic Range: region in which a species is found Habitat Patches: suitable habitat separated by areas of unsuitable habitat 42.2: Births Increase and De aths Decrease Population Size st 1 Law of Population Growth: Under constant conditions anything should grow exponentially BD Model: “Birth-Death” model of population size N t+1= N +tB – D N: Population Size B: # births D: # deaths Population Growth Rate: changes in size over time period - Change in population size can only be measured for very small populations ∆ = − ∆ Growth rates are estimated using… - Per capita birth rate ( b): # offspring produced by the avg. individual - Per capita death rate (d): average individual’s chance of dying - Per capita growth rate ( r) = (b - d) N t+1= N +t(b-d) N àtN t+1= N +trN t If b > d, then r > 0 (population grows) If b < d, then r < 0 (population shrinks) If b = d, then r = 0 (no change) ∆ - Exponential/Instantaneous Growth Rate: ∆ = 42.5: Immigration and Emigration Affect Population Dynamics Subpopulation: each patch of suitable habitat occupied by a species -­‐‑ Individuals may move between them Metapopulation: set of subpopulations in a region BIDE Model: adding the number of immigrants (I)/emigrants (E) to the BD growth model N t+1= N +tB + I - D - E - Closed Systems: no immigration/emigration; describes populations ( BD Model) - Open Systems: individuals move among subpopulations - In BD model, extinct population remains ext inct; with BIDE model, immigration can resurrect extinct 42.3: Life Histories Determine Population Growth Rates Demography: study of processes that influence birth, death and population growth Life History: sequence of key events that occ ur during individual’s life (growth, development, reproduction, death) - “Strategies that solve an ecological problem” - Covers 3 main classes of traits in organisms that contribute to overall fitness o Age/size at maturity o Number/size of offspring o Lifespan/Reproductive Investment Survivorship: fraction of individuals that survive from birth to different life stages/ages Mortality: (= 1 - survivorship) those that don’t survive from birth to life stage Fecundity: Average # of offspring each individual produces at those life stages - Increased fecundity/survivorship à Increased “r” Resources: materials/energy and time available to acquire them (in individuals & environment) - Differs from physical conditions that organisms are able to tolerate o Resources can be used up whereas conditions are experienced - Must devote some resources to activities involved in obtaining more resources Principle of Allocation: a unit of a resource can only be used for one function at a time (Ex: maintenance, growth, defense, reproduction) - Maintenance (maintaining hometostasis) is almost always first priority o In stressful conditions, majority of resources go toward maintenance o In normal conditions, more toward maintenance but others close in priority - Life-History Trade-offs: negative relationships among growth, reproduction and survival o Ex: Those that invest more in growth early in life cannot also invest in defense à Larger adult size, but lower survivorshi p 42.4: Populations Grow Multiplicatively, but the Multiplier Ca n Change Multiplicative Growth: a multiple of the population size (N) is added each period of time - Populations don’t grow multiplicatively for very long, eventually reach steady size - Doubling Time: Population doubles when the number individuals added = th e initial population at a specific time (Increases as “r” decreases; inverse relationship) 2 ▯▯▯▯▯▯ = Additive Growth: a certain number of individuals is added each period of time Density Dependent: Population density increases, r decreases (growth rate dN/dt approaches 0) - Equilibrium: when r = 0, population stops changing in size - Carrying Capacity (K): reaches equilibrium size; # of individuals an environment can support indefinitely (in closed system) o Spatial environmental factors can result in variation of “K” o Temporal variation in environmental conditions can cause populati on to fluctuate above/below “K” Exponential Growth: dN/dt = rN Logistic Growth: Carrying Capacity Factor: % of capacity left; = ▯▯▯ 100 ▯ − = = (1 − ) Assumptions: -­‐‑ “r” remains constant through time -­‐‑ All individuals are identical -­‐‑ There is no immigration or emigration (closed system) -­‐‑ There can be time lags 42.6: Ecology Provides Tools for Conse rving and Managing Populations Understanding life history strategies can be useful in managing other species - Conserving endangered species - Managing fisheries o Because fishermen prefer big fish, intense fishing reduces avg age of female fish o Younger females were smaller and produced less eggs - Reducing disease risk o Controlling abundance of rodents that are hosts is more effective than controlling abundance of deer Conservation begins with inventories of habitats/potential risks to habitat - Largest patches are given priority b/c potentially have largest populations/genetic diversity - Ability of organism to disperse between patches is evaluated - For some species, a continuous corridor of habitat is needed to connect subpopulations à allows dispersal

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Chapter 2, Problem 6 is Solved
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Textbook: Explorations in College Algebra
Edition: 5
Author: Linda Almgren Kime
ISBN: 9780470466445

This textbook survival guide was created for the textbook: Explorations in College Algebra, edition: 5. This full solution covers the following key subjects: . This expansive textbook survival guide covers 9 chapters, and 1546 solutions. The answer to “A bathtub that initially holds 50 gallons of water starts draining at 10 gallons per minute. a. Construct a function W(t) for the volume of water (in gallons) in the tub after t minutes. b. Graph the function and label the axes. Evaluate W(0) and W(5) and describe what they represent in this context. c. How would the original function and its graph change if the initial volume were 60 gallons? Call the new function U(t). d. How would the original function and graph change if the drain rate were 12 gallons per minute? Call the new function V(t). e. Add the graphs of U(t) and V(t) to the original graph of W(t)” is broken down into a number of easy to follow steps, and 113 words. The full step-by-step solution to problem: 6 from chapter: 2 was answered by , our top Math solution expert on 12/23/17, 04:55PM. Explorations in College Algebra was written by and is associated to the ISBN: 9780470466445. Since the solution to 6 from 2 chapter was answered, more than 241 students have viewed the full step-by-step answer.

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A bathtub that initially holds 50 gallons of water starts