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 6.CR, Problem 68CR
To determine
To find:
The angle
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A small company of science writers found that its rate of profit (in thousands of dollars) after t years of operation is given by P'(t) = (5t + 15) (t² + 6t+9) ³.
(a) Find the total profit in the first three years.
(b) Find the profit in the sixth year of operation.
(c) What is happening to the annual profit over the long run?
(a) The total profit in the first three years is $
(Round to the nearest dollar as needed.)
Find the area between the curves.
x= -2, x = 7, y=2x² +3, y=0
Set up the integral (or integrals) needed to compute this area. Use the smallest possible number
of integrals. Select the correct choice below and fill in the answer boxes to complete your choice.
A.
7
[[2x² +3] dx
-2
B.
[[ ] dx+
-2
7
S [ ] dx
The area between the curves is
(Simplify your answer.)
The rate at which a substance grows is given by R'(x) = 105e0.3x, where x is the time (in days).
What is the total accumulated growth during the first 2.5 days?
Set up the definite integral that determines the accumulated growth during the first 2.5 days.
2.5
Growth = (105e0.3x) dx
0
(Type exact answers in terms of e.)
Evaluate the definite integral.
Growth=
(Do not round until the final answer. Then round to one decimal place as needed.)
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
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