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In Exercises 13 40, evaluate the expression. Assume x 0.a) -43 b) (-4)3

A Survey of Mathematics with Applications | 9th Edition | ISBN: 9780321759665 | Authors: Allen R. Angel, Christine D. Abbott, Dennis C. Runde ISBN: 9780321759665 194

Solution for problem 5.1.505 Chapter 5.6

A Survey of Mathematics with Applications | 9th Edition

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A Survey of Mathematics with Applications | 9th Edition | ISBN: 9780321759665 | Authors: Allen R. Angel, Christine D. Abbott, Dennis C. Runde

A Survey of Mathematics with Applications | 9th Edition

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Problem 5.1.505

In Exercises 13 40, evaluate the expression. Assume x 0.a) -43 b) (-4)3

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M215 Midterm Lab 1: Ubiquity of Microorganism  Microbes are everywhere-this is what ubiquity is  Interior of healthy plant and animal tissues is one of the few places free of microorganisms.  No one condition or medium will permit the growth of all microorganisms.  Temperature is important for growth as well—37 for bacteria that live in bodies, 25 degrees room temp.  Also, correct atmosphere is important for bacteria that require or do not require oxygen. Definitions  Agar: a carbohydrate derived from seaweed used to solidify a liquid medium  Colony: a visible population of microorganisms growing on a solid medium.  Inoculate: to transfer organisms to a medium to initiate growth.  Media: the substances used to support the growth of microorganisms.  Pathogen: an organism capable of causing disease.  Sterile: the absence of either viable microorganisms or virsuses capable of reproduction.  Ubiquity: the existence of something everywhere at the same time. Colonial Morphology 1) Color a. White, golden, yellow, red, orange, cream, etc. 2) Appearance (Form) a. Round b. Filamentous c. irregular 3) edges or margin a. entire b. rhizoid c. lobate 4) elevation a. flat b. convex c. umbonate Lab 2- Bright-field Light Microscopy  Anton can Leeuwenhoek created first microscope—single glass lens  Disadvantages: production of distortion with increasing magnifying powers and a decrease in focal length.  Today’s microscopes: 2 lenses—ocular lens and objective lens o Ocular lens: allows comfortable viewing of the specimen from a distance o Objective lens: located near the specimen and is used to provide image magnification and image clarity. ( examples of lenses= 10x, 45x, 100x)  Total magnification is done by multiplying ocular lens by the objective lens.  Ex: 10x ocular X 45x objective = 450 total magnification  Ernst Abbe developed microscope improvements, including: condenser lens and also the lens immersion oil in place of water, and lens that reduced chromatic and spherical lens aberrations. o Condenser lens: located beneath the microscope stage and it concentrates the light emanating from the light source on the bottom side of the specimen slide. o Oil Immersion Objective: using oil as a medium for the transmission of light in order to have a more clear image. o Chromatic Lens Aberrations: thee occur because light is refracted as well as dispersed by a lens. This creates blue and red distortions of color. o Spherical Lens Aberrations: these occur because light rays passing through the edge of a convex lens are bent more than light rays passing through the center. o Apochromatic Objectives: objective lenses free of spherical and chromatic aberrations (more expensive) o Achromatic Objectives: free of chromatic lens aberrations.  Resolution: the ability of the microscope to reveal specimen structure  Magnification: the ability of the microscope to increase specimen size  Resolving Power: the ability of an objective to distinguish two nearby points as distinct and separate. (human eye = 0.1 mm/ light microscope = 0.2 um) Which is 500x better than they human eye. o Increase resolving power by decreasing wavelength + increasing NA o Blue light affords a better resolving power than red light bc its wavelength is shorter.  Numerical Aperture = n sin theta  Refractive Index = n (refers to the medium employed between the objective lens and the upper slide surface as well as the medium employed between the lower slide surface and the condenser lens) o Air= 1 o Oil= 1.25 or 1.56  Focal Length= the distance from the principal point of focus of the objective lens to the principal point of focus of the specimen. (measured in mm number 16, 4, 1.8)  The shorter the focal length the shorter the working distance (that is, the distance between the lens and the specimen) Definitions:  Achromatic objective:  Apochromatic objective:  Bright-field light microscopy  Chromatic lens aberration  Compound microscope  Condenser  Focal length  Iris diaphragm  Magnification  Numerical aperature  Parfocal  Refractive index  Resolution  Simple microscope  Spherical lens aberration  Wet mount  Working distance Class notes:  Coarse focus = 5x or 10x  Fine focus= 40x (fungus) or 100x (bacteria)  As working distance increases, the opening of the iris diaphragm decreases. Lab 3: Bright and Dark field microscopy, Wet Mount and Hanging Drop preparations  Microscopic examination allows for the determination of cell form (round/ coccus, elongate/rod, etc.), arrangement (filaments, tetrads, etc.), and cell viability.  Bright Field Microscopy and Vital Stain o Living cells appear colorless and dead cells appear blue (stained) o Dead cells are unable to enzymatically reduce the methylene blue to a colorless form like the living cells can.  Dark Field Microscopy and no stain o Living cells appear bright and dead cells appear dull.  Wet Mount Slide o Easier to prepare but dry out more rapidly. o This can be reduced by using petroleum jelly on slide o Disadvantages: false motility, inability at times to see the microorganism o “Brownian Movement”- a form of movement caused by molecules in the liquid striking a solid object, causing it to vibrate back and forth (false motility)  Hanging Drop Slide Definitions:  Dark-field microscopy:  Depression Slide:  Hanging Drop Slide:  Resting stage:  Star diaphragm:  Vital stain:  Wet mount slide: Class notes  Peritrichous  Ampitrichous  Lophotrichous Lab 4: Simple Stains, positive and negative  Simple Stain  Negative Stain- organisms are mixed with a drop of nigrosin or india ink on a slide, after drying the cells appear clear on a black background. o This technique is used to observe capsules or inclusion bodies. o Prevents eyestrain when observing multiple fields. Definitions:  Differential stain  Inclusion bodies  Micrometer  Negative stain  Parfocal  Simple stain  Smear Lab 5: Multiple and Differential Stains  Multiple stains involve at least two dyes  Also called differential stains because they specifically stain certain morphological features.  The Gram stain is especially useful because it also reveals information about the cell well (gram positive = thick PG wall, gram neg = thin PG wall) Definitions:  Counterstain  Mordant  Peptidoglycan  Vegetative cell Acid Fast Stain  Useful for identifying bacteria with a waxy lipid cell wall.  Most are members of the mycobacteria  These organisms have gram-positive cell walls, but the lipid cell wall prevents staining with gram stains.  Appearance: pink stain (on a white/clear background)  Example of bacteria this is used for: TB Capsule Stain  Used for bacteria that form capsules, which is a gelatinous coating surrounding a cell.  Consists of amino acids or carbs, which protect the bacterium from being engulfed by white blood cells.  Appearance: white halo arund the cell with a black background (because you use india ink to stain it) Endospore Stain  Endospores are resistant to most stains since it is a protective measure to keep the bacteria from harm.  Appearance: endospores appear green and vegetative cells appear pink. Storage Granule Stain  Some bacteria store materials for future use, such a s phosphate.  Appearance: granules appear darker reddish blue inside the cells. Flagellar Stain (no procedure, premade slides for us) You should be able to see the flagella and then determine which type of bacteria based on the following criteria:  Lophotrichous: a tuft of flagella at one or each end of the organism. (Spirrillum)  Peritrichous: the surface of the organism is covered with flagella (E. Coli)  Polar: a single flagellum at one or both ends of the organism (Pseudomomas) Lab 6: Pure Culture and Aseptic Technique  Goals of aseptic technique o Prevent contamination of your culture with organisms from the environment o Prevent the culture from contaminating you or others. Definitions  Aseptic  Incubate  Sterile Lab 7: Defined, Undefined, Selective, and Differential media  Defined Media: a medium that is totally made up of specific known amounts of chemicals. o Example: Glucose Salts Agar  Undefined (complex) Media: contains mixtures as yeast extract or enzymatic digests of proteins that are unknown amounts. o Also called RICH Media. o Tend to support the growth of bacteria better bc they contain more preformed nutrients and the organisms do not have to use energy and materials to synthesize the compounds supplied in the medium. o Many bacteria can only grow on these types of media o Some bacteria need many complex growth factors so they are termed fastidious. o Example: Trypticase Soy Agar  Selective Media: designed to permit some bacteria to grow but not others, so that certain bacteria can be isolated even if they constitute only a small percentage of the population.  Differential Media: also useful for isolating and identifying bacteria by observing the appearance of the colonies—if they can or cannot ferment certain sugars. o Example: EMB (both Selective and Differential) Introduction To Microbial Growth  Pure Culture: a population of bacteria that have all grown from a single cell.  Streak Plate Method: spreads individual bacteria on an agar plate.  Broth culture: useful for growing large numbers of organisms  Agar Medium: used in a petri dish when a large surface area is important  Agar Medium in tubes (slants): useful for small surface area and not drying out as fast as plates. Lab 8 : Quantification of Microorganisms  3 Common Methods to Count Bacteria o Plate Count  Based on viability of bacteria and that they will produce colonies  30-300 colonies is accuracy range that colonies can be counted on a plate  one medium cannot have all the conditions necessary to grow all bacteria present.  Takes 24 hours to obtain results to count  Two advantages:  Only viable organisms are counted  Samples with small numbers can be counted, which would have insufficient numbers for other methods o Direct Count  Used by suspending bacteria on a slie that has been ruled into squares and designed to hold a specific volume of liquid.  Counting the number in the grid area allows you to calculate total  Advantage: much faster than plating  Disadvantages:  Much be 1 x 10 organisms/ml before there are enough to be seen  Viable and nonviable organisms appear the same under a microscope o Turbidometric  Uses a spectrophotometer to measure turbidity or optical density.  The cloudier, the more bacteria.

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Chapter 5.6, Problem 5.1.505 is Solved
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Textbook: A Survey of Mathematics with Applications
Edition: 9
Author: Allen R. Angel, Christine D. Abbott, Dennis C. Runde
ISBN: 9780321759665

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In Exercises 13 40, evaluate the expression. Assume x 0.a) -43 b) (-4)3