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,
bartleby

Concept explainers

Optimization
Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the se…
Integration
Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integratio…
Application of Integration
In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.
Volume
In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects th…
Area
Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.
bartleby

Videos

Textbook Question
Book Icon
Chapter 2.3, Problem 1YT

YOUR TURN Find the growth function if 5 g grows exponentially to 18 g after 16 hours.

Expert Solution & Answer
Check Mark

Want to see the full answer?

Check out a sample textbook solution
Blurred answer
Previous
Chapter 2.2, Problem 97E
Next
Chapter 2.3, Problem 2YT

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
Knowledge Booster
Background pattern image
Calculus
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
College Algebra
Algebra
ISBN:9781938168383
Author:Jay Abramson
Publisher:OpenStax
Text book image
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Text book image
Intermediate Algebra
Algebra
ISBN:9780998625720
Author:Lynn Marecek
Publisher:OpenStax College
Text book image
College Algebra
Algebra
ISBN:9781337282291
Author:Ron Larson
Publisher:Cengage Learning
Text book image
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
Text book image
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
SEE MORE TEXTBOOKS
Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY