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find the best linear approximation to f on the interval

Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition | ISBN: 9780538735452 | Authors: David Poole ISBN: 9780538735452 298

Solution for problem 7.5.3 Chapter 7

Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition

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Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition | ISBN: 9780538735452 | Authors: David Poole

Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition

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Problem 7.5.3

find the best linear approximation to f on the interval

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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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Textbook: Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign)
Edition: 3
Author: David Poole
ISBN: 9780538735452

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find the best linear approximation to f on the interval