Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN: 9780321964038
Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher: Pearson Addison Wesley,
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Chapter 2.CR, Problem 109CR

Cancer growth Cancer cells often have a diameter of about 20 microns, or 2 10 - 5 m.

a. Although cancer cells are not exactly spheres, they are close enough to spheres to make this simplification. What is the volume of a cancer cell?

b. Suppose a cancer cells doubles every day. Starting with one cancer cell, find a formula for the total volume of the cancer cells after t days?

c. Assume that a tumor of cancer cells is roughly a sphere. Also assume that about 74 % of the tumor is made up of cancerous cells, while the rest consists of blood vessels and space between the cells. How many days must pass before the single cancer cell grows to a tumor with a diameter of 1 cm 10 - 2 m ?

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Chapter 2 Solutions

Calculus For The Life Sciences

Ch. 2.1 - YOUR TURN Solve 25x2=125x+3Ch. 2.1 - Prob. 2YTCh. 2.1 - YOUR TURN Find the amount after 4 years if 800 is...Ch. 2.1 - A ream of 20-lb paper contains 500 sheets and is...Ch. 2.1 - A ream of 20-lb paper contains 500 sheets and is...Ch. 2.1 - For Exercises 3-11, match the correct graph A-F to...Ch. 2.1 - For Exercises 3-11, match the correct graph A-F to...Ch. 2.1 - For Exercises 3-11, match the correct graph A-F to...Ch. 2.1 - For Exercises 3-11, match the correct graph A-F to...Ch. 2.1 - For Exercises 3-11, match the correct graph A-F to...
Ch. 2.1 - For Exercises 3-11, match the correct graph A-F to...Ch. 2.1 - For Exercises 3-11, match the correct graph A-F to...Ch. 2.1 - For Exercises 3-11, match the correct graph A-F to...Ch. 2.1 - For Exercises 3-11, match the correct graph A-F to...Ch. 2.1 - In Exercises3-11, there were more formulas for...Ch. 2.1 - Prob. 13ECh. 2.1 - Prob. 14ECh. 2.1 - Prob. 15ECh. 2.1 - Solve each equation. ex=1e5Ch. 2.1 - Prob. 17ECh. 2.1 - Prob. 18ECh. 2.1 - Solve each equation. 16x+3=642x-5Ch. 2.1 - Prob. 20ECh. 2.1 - Prob. 21ECh. 2.1 - Prob. 22ECh. 2.1 - Prob. 23ECh. 2.1 - Prob. 24ECh. 2.1 - Prob. 25ECh. 2.1 - Prob. 26ECh. 2.1 - Prob. 27ECh. 2.1 - Prob. 28ECh. 2.1 - Prob. 29ECh. 2.1 - Prob. 30ECh. 2.1 - Prob. 31ECh. 2.1 - Prob. 32ECh. 2.1 - Prob. 33ECh. 2.1 - Prob. 34ECh. 2.1 - Prob. 35ECh. 2.1 - A friend claims that as x becomes large, the...Ch. 2.1 - Prob. 37ECh. 2.1 - Growth of Bacteria Salmonella bacteria, found on...Ch. 2.1 - Prob. 39ECh. 2.1 - Physician Demand The demand for physicians is...Ch. 2.1 - Prob. 41ECh. 2.1 - Bacteria in Sausage The number of Enterococcus...Ch. 2.1 - Prob. 43ECh. 2.1 - Prob. 44ECh. 2.1 - Cortisone Concentration A mathematical model for...Ch. 2.1 - Prob. 46ECh. 2.1 - Prob. 47ECh. 2.1 - Prob. 48ECh. 2.1 - Prob. 50ECh. 2.1 - Interest Find the interest earned on 10,000...Ch. 2.1 - Prob. 52ECh. 2.1 - Interest Ron Hampton needs to choose between two...Ch. 2.1 - Prob. 54ECh. 2.1 - Prob. 55ECh. 2.1 - Prob. 56ECh. 2.1 - Interest Leigh Jacks plans to invest 500 into a...Ch. 2.1 - Prob. 58ECh. 2.1 - Prob. 59ECh. 2.1 - Interest On January 1, 2000, Jack deposited 1000...Ch. 2.2 - YOUR TURN Write the equation in logarithmic...Ch. 2.2 - Prob. 2YTCh. 2.2 - YOUR TURN Write the expression logax2/y3 as a sum,...Ch. 2.2 - Prob. 4YTCh. 2.2 - YOUR TURN Solve for x: log2x+log2x+2=3Ch. 2.2 - YOUR TURN 6 Solve for x: 2x+1=3xCh. 2.2 - Prob. 7YTCh. 2.2 - Write each exponential equation in logarithmic...Ch. 2.2 - Prob. 2ECh. 2.2 - Write each exponential equation in logarithmic...Ch. 2.2 - Prob. 4ECh. 2.2 - Prob. 5ECh. 2.2 - Prob. 6ECh. 2.2 - Prob. 7ECh. 2.2 - Prob. 8ECh. 2.2 - Prob. 9ECh. 2.2 - Prob. 10ECh. 2.2 - Prob. 11ECh. 2.2 - Prob. 12ECh. 2.2 - Prob. 13ECh. 2.2 - Evaluate each logarithm without using a...Ch. 2.2 - Prob. 15ECh. 2.2 - Prob. 16ECh. 2.2 - Prob. 17ECh. 2.2 - Prob. 18ECh. 2.2 - Prob. 19ECh. 2.2 - Prob. 20ECh. 2.2 - Prob. 21ECh. 2.2 - Prob. 22ECh. 2.2 - Prob. 23ECh. 2.2 - Prob. 24ECh. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - Prob. 28ECh. 2.2 - Prob. 29ECh. 2.2 - Prob. 30ECh. 2.2 - Prob. 31ECh. 2.2 - Prob. 32ECh. 2.2 - Prob. 33ECh. 2.2 - Suppose logb2=a and logb3=c. Use the properties of...Ch. 2.2 - Prob. 35ECh. 2.2 - Prob. 36ECh. 2.2 - Prob. 37ECh. 2.2 - Prob. 38ECh. 2.2 - Prob. 39ECh. 2.2 - Prob. 40ECh. 2.2 - Prob. 41ECh. 2.2 - Prob. 42ECh. 2.2 - Prob. 43ECh. 2.2 - Prob. 44ECh. 2.2 - Prob. 45ECh. 2.2 - Prob. 46ECh. 2.2 - Prob. 47ECh. 2.2 - Prob. 48ECh. 2.2 - Prob. 49ECh. 2.2 - Prob. 50ECh. 2.2 - Prob. 51ECh. 2.2 - Prob. 52ECh. 2.2 - Prob. 53ECh. 2.2 - Prob. 54ECh. 2.2 - Prob. 55ECh. 2.2 - Prob. 56ECh. 2.2 - Prob. 57ECh. 2.2 - Prob. 58ECh. 2.2 - Prob. 59ECh. 2.2 - Prob. 60ECh. 2.2 - Prob. 61ECh. 2.2 - Prob. 62ECh. 2.2 - Solve each question in Exercises 41-64. Round...Ch. 2.2 - Solve each question in Exercises 41-64. Round...Ch. 2.2 - Write each expression using base e rather than...Ch. 2.2 - Prob. 66ECh. 2.2 - Prob. 67ECh. 2.2 - Approximate each expression in the form ax without...Ch. 2.2 - Prob. 69ECh. 2.2 - Prob. 70ECh. 2.2 - Prob. 71ECh. 2.2 - Prob. 72ECh. 2.2 - Prob. 73ECh. 2.2 - Prob. 74ECh. 2.2 - Prob. 75ECh. 2.2 - Prob. 76ECh. 2.2 - Minority Population The U.S. Census Bureau has...Ch. 2.2 - Bald Eagle Population The U.S. Fish & Wildlife...Ch. 2.2 - Population Growth Two species of squirrels inhabit...Ch. 2.2 - Population Growth In July 1994, the population of...Ch. 2.2 - Prob. 81ECh. 2.2 - Prob. 82ECh. 2.2 - Find the value of the index of diversity for...Ch. 2.2 - Prob. 84ECh. 2.2 - Prob. 85ECh. 2.2 - Prob. 86ECh. 2.2 - Drug Concentration When a pharmaceutical drug is...Ch. 2.2 - Tumor Growth An article on growth rates of cancer...Ch. 2.2 - Prob. 89ECh. 2.2 - Prob. 90ECh. 2.2 - Torontos Jewish Population The table gives the...Ch. 2.2 - OTHER APPLICATIONS Music Theory A music theorist...Ch. 2.2 - OTHER APPLICATIONS Evolution of languages The...Ch. 2.2 - Prob. 94ECh. 2.2 - Prob. 95ECh. 2.2 - Earthquake Intensity The magnitude of an...Ch. 2.2 - Acidity of a solution A common measure for the...Ch. 2.3 - YOUR TURN Find the growth function if 5 g grows...Ch. 2.3 - Prob. 2YTCh. 2.3 - In the exponential growth or decay function...Ch. 2.3 - Prob. 2ECh. 2.3 - Prob. 3ECh. 2.3 - Prob. 4ECh. 2.3 - Prob. 5ECh. 2.3 - Prob. 6ECh. 2.3 - Giardia When a person swallows giardia cysts,...Ch. 2.3 - Growth of Bacteria A culture contains 25,000...Ch. 2.3 - Decrease in Bacteria When an antibiotic is...Ch. 2.3 - Growth of Bacteria The growth of bacteria in food...Ch. 2.3 - Prob. 11ECh. 2.3 - Chromosomal Abnormality The graph below shows how...Ch. 2.3 - Botany A group of Tasmanian botanists have claimed...Ch. 2.3 - Decay of Radioactivity A large cloud of...Ch. 2.3 - Prob. 15ECh. 2.3 - Prob. 16ECh. 2.3 - Carbon Dating Refer to Example 2. A sample from a...Ch. 2.3 - Half Life Find the half-life of each radioactive...Ch. 2.3 - Half Life Find the half life of each radioactive...Ch. 2.3 - Half-Life The half-life of plutonium-241 is...Ch. 2.3 - Half-Life The half-life of radium-226 is...Ch. 2.3 - Radioactive Decay 500 g of iodine-131 is decaying...Ch. 2.3 - Radioactive Decay 25 g of polonium-210 is decaying...Ch. 2.3 - Nuclear Energy Nuclear energy derived from...Ch. 2.3 - Chemical Dissolution The amount of chemical that...Ch. 2.3 - Newtons Law of Cooling Newtons law of cooling says...Ch. 2.3 - Newtons Law of Cooling Newtons law of cooling says...Ch. 2.3 - Newtons Law of Cooling Newtons law of cooling says...Ch. 2.4 - YOUR TURN a Convert 210 to radians. b Convert 3/4...Ch. 2.4 - Prob. 2YTCh. 2.4 - Prob. 3YTCh. 2.4 - Prob. 4YTCh. 2.4 - Prob. 5YTCh. 2.4 - Prob. 1ECh. 2.4 - Prob. 2ECh. 2.4 - Convert the following degree measures to radians....Ch. 2.4 - Prob. 4ECh. 2.4 - Prob. 5ECh. 2.4 - Prob. 6ECh. 2.4 - Prob. 7ECh. 2.4 - Prob. 8ECh. 2.4 - Prob. 9ECh. 2.4 - Prob. 10ECh. 2.4 - Prob. 11ECh. 2.4 - Prob. 12ECh. 2.4 - Prob. 13ECh. 2.4 - Prob. 14ECh. 2.4 - Convert the following radian measures to degrees....Ch. 2.4 - Prob. 16ECh. 2.4 - Prob. 17ECh. 2.4 - Prob. 18ECh. 2.4 - Prob. 19ECh. 2.4 - Prob. 20ECh. 2.4 - Prob. 21ECh. 2.4 - Prob. 22ECh. 2.4 - Prob. 23ECh. 2.4 - Prob. 24ECh. 2.4 - For Exercises 2532, complete the following table....Ch. 2.4 - Prob. 26ECh. 2.4 - Prob. 27ECh. 2.4 - Prob. 28ECh. 2.4 - Prob. 29ECh. 2.4 - For Exercises 2532, complete the following table....Ch. 2.4 - Prob. 31ECh. 2.4 - Prob. 32ECh. 2.4 - Find the following function values without a...Ch. 2.4 - Find the following function values without a...Ch. 2.4 - Prob. 35ECh. 2.4 - Prob. 36ECh. 2.4 - Prob. 37ECh. 2.4 - Prob. 38ECh. 2.4 - Find the following function values without a...Ch. 2.4 - Prob. 40ECh. 2.4 - Find the following function values without a...Ch. 2.4 - Find the following function values without a...Ch. 2.4 - Find the following function values without using a...Ch. 2.4 - Find the following function values without using a...Ch. 2.4 - Find the following function values without using a...Ch. 2.4 - Find the following function values without using a...Ch. 2.4 - Find the following function values without using a...Ch. 2.4 - Find the following function values without using a...Ch. 2.4 - Find all values of x between 0 and 2 that satisfy...Ch. 2.4 - Find all values of x between 0 and 2 that satisfy...Ch. 2.4 - Find all values of x between 0 and 2 that satisfy...Ch. 2.4 - Find all values of x between 0 and 2 that satisfy...Ch. 2.4 - Prob. 53ECh. 2.4 - Prob. 54ECh. 2.4 - Prob. 55ECh. 2.4 - Prob. 56ECh. 2.4 - Prob. 57ECh. 2.4 - Prob. 58ECh. 2.4 - Prob. 59ECh. 2.4 - Use a calculator to find the following function...Ch. 2.4 - Prob. 61ECh. 2.4 - Prob. 62ECh. 2.4 - Find the amplitude a and period T of each...Ch. 2.4 - Find the amplitude a and period T of each...Ch. 2.4 - Find the amplitude a and period T of each...Ch. 2.4 - Find the amplitude a and period T of each...Ch. 2.4 - Graph each function defined as follows over a...Ch. 2.4 - Graph each function defined as follows over a...Ch. 2.4 - Graph each function defined as follows over a...Ch. 2.4 - Graph each function defined as follows over a...Ch. 2.4 - Graph each function defined as follows over a...Ch. 2.4 - Graph each function defined as follows over a...Ch. 2.4 - Graph each function defined as follows over a...Ch. 2.4 - Graph each function defined as follows over a...Ch. 2.4 - Prob. 75ECh. 2.4 - Prob. 76ECh. 2.4 - Prob. 77ECh. 2.4 - Transylvania Hypothesis The Transylvania...Ch. 2.4 - Prob. 79ECh. 2.4 - Prob. 80ECh. 2.4 - Prob. 81ECh. 2.4 - Prob. 82ECh. 2.4 - Prob. 83ECh. 2.4 - Prob. 84ECh. 2.4 - Prob. 85ECh. 2.4 - Prob. 86ECh. 2.4 - Sound Suppose the A key above Middle C is played...Ch. 2.4 - Temperature The maximum afternoon temperature in...Ch. 2.4 - Temperature A mathematical model for the...Ch. 2.4 - Prob. 90ECh. 2.4 - Prob. 91ECh. 2.4 - Prob. 92ECh. 2.CR - Prob. 1CRCh. 2.CR - Prob. 2CRCh. 2.CR - Prob. 3CRCh. 2.CR - Prob. 4CRCh. 2.CR - Determine whether each of the following statement...Ch. 2.CR - Prob. 6CRCh. 2.CR - Prob. 7CRCh. 2.CR - Prob. 8CRCh. 2.CR - Prob. 9CRCh. 2.CR - Prob. 10CRCh. 2.CR - Prob. 11CRCh. 2.CR - Prob. 12CRCh. 2.CR - Prob. 13CRCh. 2.CR - Prob. 14CRCh. 2.CR - Prob. 15CRCh. 2.CR - Prob. 16CRCh. 2.CR - Prob. 17CRCh. 2.CR - Prob. 18CRCh. 2.CR - Prob. 19CRCh. 2.CR - Prob. 20CRCh. 2.CR - Prob. 21CRCh. 2.CR - Prob. 22CRCh. 2.CR - Prob. 23CRCh. 2.CR - Prob. 24CRCh. 2.CR - Prob. 25CRCh. 2.CR - Prob. 26CRCh. 2.CR - Prob. 27CRCh. 2.CR - Prob. 28CRCh. 2.CR - Prob. 29CRCh. 2.CR - Prob. 30CRCh. 2.CR - Prob. 31CRCh. 2.CR - Prob. 32CRCh. 2.CR - Prob. 33CRCh. 2.CR - Prob. 34CRCh. 2.CR - Prob. 35CRCh. 2.CR - Prob. 36CRCh. 2.CR - Prob. 37CRCh. 2.CR - Prob. 38CRCh. 2.CR - Prob. 39CRCh. 2.CR - Prob. 40CRCh. 2.CR - Prob. 41CRCh. 2.CR - Prob. 42CRCh. 2.CR - Prob. 43CRCh. 2.CR - Prob. 44CRCh. 2.CR - Prob. 45CRCh. 2.CR - Prob. 46CRCh. 2.CR - Prob. 47CRCh. 2.CR - Prob. 48CRCh. 2.CR - Prob. 49CRCh. 2.CR - Prob. 50CRCh. 2.CR - Prob. 51CRCh. 2.CR - Prob. 52CRCh. 2.CR - Prob. 53CRCh. 2.CR - Prob. 54CRCh. 2.CR - Prob. 55CRCh. 2.CR - Prob. 56CRCh. 2.CR - Prob. 57CRCh. 2.CR - Prob. 58CRCh. 2.CR - Prob. 59CRCh. 2.CR - Prob. 60CRCh. 2.CR - Prob. 61CRCh. 2.CR - Prob. 62CRCh. 2.CR - Prob. 63CRCh. 2.CR - Prob. 64CRCh. 2.CR - Prob. 65CRCh. 2.CR - Prob. 66CRCh. 2.CR - Prob. 67CRCh. 2.CR - Prob. 68CRCh. 2.CR - Prob. 69CRCh. 2.CR - Prob. 70CRCh. 2.CR - Prob. 71CRCh. 2.CR - Prob. 72CRCh. 2.CR - Prob. 73CRCh. 2.CR - Prob. 74CRCh. 2.CR - Prob. 75CRCh. 2.CR - Prob. 76CRCh. 2.CR - Prob. 77CRCh. 2.CR - Prob. 78CRCh. 2.CR - Prob. 79CRCh. 2.CR - Prob. 80CRCh. 2.CR - Prob. 81CRCh. 2.CR - Prob. 82CRCh. 2.CR - Prob. 83CRCh. 2.CR - Prob. 84CRCh. 2.CR - Prob. 85CRCh. 2.CR - Prob. 86CRCh. 2.CR - Prob. 87CRCh. 2.CR - Prob. 88CRCh. 2.CR - Prob. 89CRCh. 2.CR - Prob. 90CRCh. 2.CR - Find each function value without using a...Ch. 2.CR - Prob. 92CRCh. 2.CR - Prob. 93CRCh. 2.CR - Prob. 94CRCh. 2.CR - Prob. 95CRCh. 2.CR - Prob. 96CRCh. 2.CR - Prob. 97CRCh. 2.CR - Prob. 98CRCh. 2.CR - Prob. 99CRCh. 2.CR - Prob. 100CRCh. 2.CR - Prob. 101CRCh. 2.CR - Prob. 102CRCh. 2.CR - Prob. 103CRCh. 2.CR - Prob. 104CRCh. 2.CR - Prob. 105CRCh. 2.CR - Prob. 106CRCh. 2.CR - Glucose Concentration When glucose is infused into...Ch. 2.CR - Prob. 108CRCh. 2.CR - Cancer growth Cancer cells often have a diameter...Ch. 2.CR - Prob. 110CRCh. 2.CR - Respiratory Rate Researchers have found that the...Ch. 2.CR - Prob. 112CRCh. 2.CR - Prob. 113CRCh. 2.CR - Prob. 114CRCh. 2.CR - Prob. 115CRCh. 2.CR - Prob. 116CRCh. 2.CR - Prob. 117CRCh. 2.CR - Prob. 118CRCh. 2.CR - Prob. 119CRCh. 2.CR - Prob. 120CRCh. 2.CR - Prob. 121CRCh. 2.CR - Prob. 122CRCh. 2.CR - Prob. 123CRCh. 2.CR - Prob. 124CRCh. 2.CR - Prob. 125CRCh. 2.CR - Prob. 126CRCh. 2.CR - Temperature The table lists the average monthly...Ch. 2.EA - Determine whether each of the following statement...Ch. 2.EA - Prob. 2EA
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