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

Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …
bartleby

Videos

Textbook Question
Book Icon
Chapter 6.4, Problem 27E

LIFE SCIENCE APPLICATION

Shadow Length A man 6 ft tall is walking away from a lamp post at the rate of 50 ft per minute. When the man is 8 ft from the lamp post, his shadow is 10 ft long. Find the rate at which the length of the shadow is increasing when he is 25 ft from the lamp post. (See the figure.)

Expert Solution & Answer
Check Mark

Want to see the full answer?

Check out a sample textbook solution
Blurred answer
Previous
Chapter 6.4, Problem 26E
Next
Chapter 6.4, Problem 28E
Students have asked these similar questions
Graph y= log(x − 1) +4 10+ 9 8 7 6 5 4 32 1 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -1 6 7 8 9 10 -2 -3 -4 -5 -6 -7 -8 -9 -10
Write an equation for the graph shown below. 5 4 3 2 1 -5-4-3-2-1 -1 1 2 3 4 5 f(x) = -2 -3 -4 -5
1. We want to graph the function f(x) log4 x. In a table below, = find at three points with nice integer y-values (no rounding!) and then graph the function at right. Be sure to clearly indicate any asymptotes. (4 points) 3 2 1- -1 0 1 2 3 4 5 10 X log4(x) -1 -2 -3- 6 7 8 00

Chapter 6 Solutions

Calculus For The Life Sciences

Ch. 6.1 - YOUR TURN Find the absolute extrema of the...Ch. 6.1 - Prob. 2YTCh. 6.1 - EXERCISES Find the locations of any absolute...Ch. 6.1 - EXERCISES Find the locations of any absolute...Ch. 6.1 - Prob. 3ECh. 6.1 - Prob. 4ECh. 6.1 - Prob. 5ECh. 6.1 - EXERCISES Find the locations of any absolute...Ch. 6.1 - EXERCISES Find the locations of any absolute...Ch. 6.1 - Prob. 8E
Ch. 6.1 - EXERCISES What is the difference between a...Ch. 6.1 - Prob. 11ECh. 6.1 - Prob. 12ECh. 6.1 - Prob. 13ECh. 6.1 - Prob. 14ECh. 6.1 - Prob. 15ECh. 6.1 - EXERCISES Find the absolute extrema if they exist,...Ch. 6.1 - Prob. 17ECh. 6.1 - Prob. 18ECh. 6.1 - Prob. 19ECh. 6.1 - Prob. 20ECh. 6.1 - Prob. 21ECh. 6.1 - Prob. 22ECh. 6.1 - EXERCISES Find the absolute extrema if they exist,...Ch. 6.1 - Prob. 24ECh. 6.1 - Prob. 25ECh. 6.1 - Prob. 26ECh. 6.1 - Prob. 27ECh. 6.1 - EXERCISES Find the absolute extrema if they exist,...Ch. 6.1 - Find the absolute extrema if they exist, as well...Ch. 6.1 - Prob. 30ECh. 6.1 - EXERCISES Graph each function on the indicated...Ch. 6.1 - Prob. 32ECh. 6.1 - Prob. 33ECh. 6.1 - Prob. 34ECh. 6.1 - Prob. 35ECh. 6.1 - EXERCISES Find the absolute extrema if they exist,...Ch. 6.1 - Prob. 37ECh. 6.1 - Prob. 38ECh. 6.1 - Prob. 39ECh. 6.1 - Prob. 40ECh. 6.1 - Prob. 41ECh. 6.1 - EXERCISES Let f(x)=e2x, For x0, let P(x) be the...Ch. 6.1 - Prob. 43ECh. 6.1 - EXERCISES Salmon Spawning The number of salmon...Ch. 6.1 - Prob. 45ECh. 6.1 - EXERCISES Fungal growth Because of the time that...Ch. 6.1 - EXERCISES Dentin Growth The growth of dentin in...Ch. 6.1 - Prob. 48ECh. 6.1 - Prob. 49ECh. 6.1 - EXERCISES Satisfaction Suppose some substance such...Ch. 6.1 - EXERCISES Area A piece of wire 12 ft long is cut...Ch. 6.1 - EXERCISES Area A piece of wire 12 ft long is cut...Ch. 6.1 - EXERCISES Area A piece of wire 12 ft long is cut...Ch. 6.1 - Prob. 54ECh. 6.1 - Prob. 56ECh. 6.1 - Prob. 57ECh. 6.1 - Prob. 58ECh. 6.2 - Find two nonnegative number x and y for which...Ch. 6.2 - YOUR TURN Suppose the animal in Example 2 can run...Ch. 6.2 - YOUR TURN Repeat Example 3 using an 8m by 8m piece...Ch. 6.2 - YOUR TURN Repeat Example 4 if the volume is to be...Ch. 6.2 - Prob. 1ECh. 6.2 - EXERCISES In Exercises 1-4, use the steps shown in...Ch. 6.2 - EXERCISES In Exercises 1-4, use the steps shown in...Ch. 6.2 - Prob. 4ECh. 6.2 - Prob. 5ECh. 6.2 - EXERCISES Disease Another disease hits the...Ch. 6.2 - EXERCISES Maximum Sustainable Harvest Find the...Ch. 6.2 - EXERCISES Maximum Sustainable Harvest Find the...Ch. 6.2 - EXERCISES Pollution A lake polluted by bacteria is...Ch. 6.2 - Prob. 10ECh. 6.2 - Maximum Sustainable Harvest In Exercise 11 and 12,...Ch. 6.2 - Maximum Sustainable Harvest In Exercise 11 and 12,...Ch. 6.2 - Prob. 13ECh. 6.2 - Pigeon Flight Repeat Exercise 13, but assume a...Ch. 6.2 - Applications of Extrema Bird Migration Suppose a...Ch. 6.2 - Prob. 17ECh. 6.2 - Prob. 19ECh. 6.2 - Applications of Extrema OTHER APPLICATIONS Area A...Ch. 6.2 - Prob. 21ECh. 6.2 - Prob. 22ECh. 6.2 - Prob. 23ECh. 6.2 - OTHER APPLICATIONS Cost with Fixed Area A fence...Ch. 6.2 - OTHER APPLICATIONS Packaging Design An exercise...Ch. 6.2 - OTHER APPLICATIONS Packaging Design A company...Ch. 6.2 - OTHER APPLICATIONS Container Design An open box...Ch. 6.2 - OTHER APPLICATIONS Container Design Consider the...Ch. 6.2 - OTHER APPLICATIONS Packaging Cost A closed box...Ch. 6.2 - Prob. 31ECh. 6.2 - Prob. 32ECh. 6.2 - Prob. 33ECh. 6.2 - Packaging Design A cylindrical box will be tied up...Ch. 6.2 - Cost A company wishes to run a utility cable from...Ch. 6.2 - Cost Repeat Exercise 38, but make point A 7 miles...Ch. 6.2 - Prob. 40ECh. 6.2 - Travel Time Repeat Example 40, but assume the...Ch. 6.2 - Postal Regulations The U.S. postal service...Ch. 6.2 - Ladder A thief tries to enter a building by...Ch. 6.2 - Ladder A janitor in a hospital needs to carry a...Ch. 6.3 - Find dydx if x2+y2=xy.Ch. 6.3 - Prob. 2YTCh. 6.3 - Your Turn The graph of y4x4y2+x2=0 is called the...Ch. 6.3 - Prob. 1ECh. 6.3 - Prob. 2ECh. 6.3 - Find dydxby implicit differentiation for the...Ch. 6.3 - Prob. 4ECh. 6.3 - Prob. 5ECh. 6.3 - Prob. 6ECh. 6.3 - Prob. 7ECh. 6.3 - Prob. 8ECh. 6.3 - Find dy/dxby implicit differentiation for the...Ch. 6.3 - Find dy/dxby implicit differentiation for the...Ch. 6.3 - Prob. 11ECh. 6.3 - Prob. 12ECh. 6.3 - Prob. 13ECh. 6.3 - EXERCISES Find dy/dxby implicit differentiation...Ch. 6.3 - Find dy/dxby implicit differentiation for the...Ch. 6.3 - Prob. 16ECh. 6.3 - EXERCISES Find dy/dxby implicit differentiation...Ch. 6.3 - Prob. 18ECh. 6.3 - EXERCISES Find the equation of the tangent line at...Ch. 6.3 - Prob. 20ECh. 6.3 - Prob. 21ECh. 6.3 - Prob. 22ECh. 6.3 - Prob. 23ECh. 6.3 - Prob. 24ECh. 6.3 - Prob. 25ECh. 6.3 - Prob. 26ECh. 6.3 - Find the equation of the tangent line at the given...Ch. 6.3 - Prob. 28ECh. 6.3 - Prob. 29ECh. 6.3 - Prob. 30ECh. 6.3 - Prob. 31ECh. 6.3 - Prob. 32ECh. 6.3 - Prob. 33ECh. 6.3 - Prob. 34ECh. 6.3 - Prob. 35ECh. 6.3 - Prob. 36ECh. 6.3 - Information on curve in Exercise 37-40, as well as...Ch. 6.3 - Information on curve in Exercise 37-40, as well as...Ch. 6.3 - Prob. 39ECh. 6.3 - Prob. 40ECh. 6.3 - Prob. 41ECh. 6.3 - Prob. 42ECh. 6.3 - Prob. 43ECh. 6.3 - Prob. 44ECh. 6.3 - Prob. 45ECh. 6.3 - Prob. 46ECh. 6.3 - Biochemical Reaction A simple biochemical reaction...Ch. 6.3 - Species The relationship between the number of...Ch. 6.3 - Prob. 49ECh. 6.3 - Prob. 50ECh. 6.3 - Prob. 51ECh. 6.3 - Prob. 52ECh. 6.3 - Prob. 53ECh. 6.4 - YOUR TURN Suppose x are y are both functions of t...Ch. 6.4 - YOUR TURN A 25ft ladder is placed against a...Ch. 6.4 - Prob. 3YTCh. 6.4 - Repeat Example 5 using the daily demand function...Ch. 6.4 - Assume x and y are functions of t. Evaluate...Ch. 6.4 - Assume x and y are functions of t. Evaluate...Ch. 6.4 - Assume x and y are functions of t. Evaluate...Ch. 6.4 - Assume x and y are functions of t. Evaluate...Ch. 6.4 - Assume x and y are functions of t. Evaluate...Ch. 6.4 - Prob. 6ECh. 6.4 - Prob. 7ECh. 6.4 - Assume xand yare functions of t.Evaluate dy/dtfor...Ch. 6.4 - Assume xand yare functions of t.Evaluate dy/dtfor...Ch. 6.4 - Prob. 10ECh. 6.4 - Prob. 11ECh. 6.4 - Prob. 12ECh. 6.4 - LIFE SCIENCE APPLICATIONS Brain Mass The brain...Ch. 6.4 - Prob. 14ECh. 6.4 - LIFE SCIENCE APPLICATIONS Metabolic Rate The...Ch. 6.4 - LIFE SCIENCE APPLICATIONS Metabolic Rate The...Ch. 6.4 - Lizards The energy cost of horizontal locomotion...Ch. 6.4 - Prob. 18ECh. 6.4 - Crime Rate Sociologists have found that crime...Ch. 6.4 - Memorization Skills Under certain conditions, a...Ch. 6.4 - Sliding Ladder A 17-ft ladder is placed against a...Ch. 6.4 - Distance a. One car leaves a given point and...Ch. 6.4 - AreaA rock is thrown into a still pond. The...Ch. 6.4 - A spherical snowball is placed in the sun. The sun...Ch. 6.4 - Ice CubeAn ice cube that is 3 cm on each side is...Ch. 6.4 - Prob. 26ECh. 6.4 - LIFE SCIENCE APPLICATION Shadow Length A man 6 ft...Ch. 6.4 - LIFE SCIENCE APPLICATION Water Level A trough has...Ch. 6.4 - Prob. 29ECh. 6.4 - LIFE SCIENCE APPLICATION Kite Flying Christine...Ch. 6.4 - Prob. 31ECh. 6.4 - Prob. 32ECh. 6.4 - Prob. 33ECh. 6.4 - Prob. 34ECh. 6.4 - Rotating Lighthouse The beacon on a lighthouse 50m...Ch. 6.4 - Rotating Camera A television camera on a tripod...Ch. 6.5 - YOUR TURN Find dy if y=300x23,x=8, and dx=0.05.Ch. 6.5 - Prob. 2YTCh. 6.5 - YOUR TURN Repeat Example 4 for r=1.25mm with a...Ch. 6.5 - Prob. 1ECh. 6.5 - Prob. 2ECh. 6.5 - Prob. 3ECh. 6.5 - Prob. 4ECh. 6.5 - For Exercises 1-8, find dyfor the given values of...Ch. 6.5 - Differentials: Linear Approximation For Exercises...Ch. 6.5 - Differentials: Linear Approximation For Exercises...Ch. 6.5 - Prob. 8ECh. 6.5 - Prob. 9ECh. 6.5 - Prob. 10ECh. 6.5 - Prob. 11ECh. 6.5 - Use the differential to approximate each quantity....Ch. 6.5 - Prob. 13ECh. 6.5 - Use the differential to approximate each quantity....Ch. 6.5 - Prob. 15ECh. 6.5 - Prob. 16ECh. 6.5 - Prob. 17ECh. 6.5 - Use the differential to approximate each quantity....Ch. 6.5 - Prob. 19ECh. 6.5 - Prob. 20ECh. 6.5 - LIFE SCIENCE APPLICATIONS Bacteria Population The...Ch. 6.5 - Prob. 22ECh. 6.5 - Prob. 23ECh. 6.5 - LIFE SCIENCE APPLICATIONS Area of an Oil Slick An...Ch. 6.5 - LIFE SCIENCE APPLICATIONS Area of a Bacteria...Ch. 6.5 - Prob. 26ECh. 6.5 - LIFE SCIENCE APPLICATIONS Pigs Researchers have...Ch. 6.5 - Prob. 28ECh. 6.5 - OTHER APPLICATIONS Volume A spherical snowball is...Ch. 6.5 - Prob. 30ECh. 6.5 - Prob. 31ECh. 6.5 - Prob. 32ECh. 6.5 - Prob. 33ECh. 6.5 - Prob. 34ECh. 6.5 - Prob. 35ECh. 6.5 - Tolerance A worker is constructing a cubical box...Ch. 6.5 - Measurement Error A cone has a known height of...Ch. 6.5 - Material Requirement A cube 4in. on an edge is...Ch. 6.5 - Material Requirement Beach balls 1ft in diameter...Ch. 6.CR - Prob. 1CRCh. 6.CR - Prob. 2CRCh. 6.CR - Prob. 3CRCh. 6.CR - Determine whether each of the following statements...Ch. 6.CR - Determine whether each of the following statements...Ch. 6.CR - Determine whether each of the following statements...Ch. 6.CR - Determine whether each of the following statements...Ch. 6.CR - Prob. 8CRCh. 6.CR - Prob. 9CRCh. 6.CR - Prob. 10CRCh. 6.CR - Prob. 11CRCh. 6.CR - Prob. 12CRCh. 6.CR - Prob. 13CRCh. 6.CR - Prob. 14CRCh. 6.CR - Prob. 15CRCh. 6.CR - Prob. 16CRCh. 6.CR - Prob. 18CRCh. 6.CR - Prob. 19CRCh. 6.CR - Prob. 20CRCh. 6.CR - Prob. 21CRCh. 6.CR - Prob. 22CRCh. 6.CR - Prob. 23CRCh. 6.CR - Prob. 24CRCh. 6.CR - Prob. 25CRCh. 6.CR - Prob. 26CRCh. 6.CR - Prob. 27CRCh. 6.CR - Prob. 28CRCh. 6.CR - Prob. 29CRCh. 6.CR - Prob. 30CRCh. 6.CR - Prob. 31CRCh. 6.CR - Prob. 32CRCh. 6.CR - Prob. 33CRCh. 6.CR - Prob. 34CRCh. 6.CR - Prob. 35CRCh. 6.CR - Prob. 36CRCh. 6.CR - Prob. 37CRCh. 6.CR - Prob. 38CRCh. 6.CR - Prob. 39CRCh. 6.CR - Prob. 40CRCh. 6.CR - Prob. 41CRCh. 6.CR - Prob. 42CRCh. 6.CR - Prob. 43CRCh. 6.CR - Prob. 44CRCh. 6.CR - Prob. 45CRCh. 6.CR - Prob. 46CRCh. 6.CR - Prob. 47CRCh. 6.CR - Prob. 48CRCh. 6.CR - Prob. 49CRCh. 6.CR - Prob. 50CRCh. 6.CR - Prob. 53CRCh. 6.CR - Prob. 54CRCh. 6.CR - OTHER APPLICATIONS Sliding Ladder A 50-ft ladder...Ch. 6.CR - Prob. 56CRCh. 6.CR - Prob. 57CRCh. 6.CR - Prob. 58CRCh. 6.CR - Prob. 59CRCh. 6.CR - Prob. 60CRCh. 6.CR - Prob. 61CRCh. 6.CR - Prob. 62CRCh. 6.CR - Prob. 63CRCh. 6.CR - Prob. 64CRCh. 6.CR - Prob. 65CRCh. 6.CR - Prob. 66CRCh. 6.CR - Prob. 67CRCh. 6.CR - Prob. 68CRCh. 6.EA - In this application, we set up a mathematical...Ch. 6.EA - Prob. 2EACh. 6.EA - Prob. 3EACh. 6.EA - Prob. 4EACh. 6.EA - Prob. 5EACh. 6.EA - Prob. 6EA
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
Elementary Algebra
Algebra
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:OpenStax - Rice University
Text book image
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,
Text book image
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Text book image
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Text book image
College Algebra
Algebra
ISBN:9781337282291
Author:Ron Larson
Publisher:Cengage Learning
Text book image
College Algebra
Algebra
ISBN:9781938168383
Author:Jay Abramson
Publisher:OpenStax
SEE MORE TEXTBOOKS
Finding Local Maxima and Minima by Differentiation; Author: Professor Dave Explains;https://www.youtube.com/watch?v=pvLj1s7SOtk;License: Standard YouTube License, CC-BY