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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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Question
Chapter 11.6, Problem 8E
To determine
To find:
The equation which represents the number of people who heard the news in t day. And also find the number of people who heard the news in 3 days.
Expert Solution & Answer
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Students have asked these similar questions
A ladder 27 feet long leans against a wall and the foot of the ladder is sliding away at a constant rate of 3 feet/sec. Meanwhile, a firefighter is climbing up the ladder at a rate of 2 feet/sec. When the firefighter has climbed up 6 feet of the ladder, the ladder makes an angle of л/3 with the ground. Answer the two related
rates questions below. (Hint: Use two carefully labeled similar right triangles.)
(a) If h is the height of the firefighter above the ground, at the instant the angle of the ladder with the ground is л/3, find dh/dt=
feet/sec.
(b) If w is the horizontal distance from the firefighter to the wall, at the instant the angle of the ladder with the ground is л/3, find dw/dt=
feet/sec.
Two cars start moving from the same point. One travels south at 60 mi/h and the other travels west at 25 mi/h. At what rate (in mi/h) is the distance between the cars increasing four hours later?
Step 1
Using the diagram of a right triangle given below, the relation between x, y, and z is
z²
= x²+
+12
x
Step 2
We must find dz/dt. Differentiating both sides and simplifying gives us the following.
2z
dz
dt
dx
2x.
+2y
dt
dx
dy
dz
x
+y
dt
dt
dt
2z
dy
dt
×
dx
(x+y
dt
dy
dt
An elastic rope is attached to the ground at the positions shown in the picture. The rope is being pulled up along the dotted line. Assume the units are meters.
9
ground level
Assume that x is increasing at a rate of 3 meters/sec.
(a) Write as a function of x: 0=
(b) When x=10, the angle is changing at a rate of
rad/sec.
(c) Let L be the the left hand piece of rope and R the right hand piece of rope. When x=10, is the rate of change of L larger than the rate of change of R?
○ Yes
○ No
Chapter 11 Solutions
Calculus For The Life Sciences
Ch. 11.1 - YOUR TURN 1 Find all solutions of the differential...Ch. 11.1 - Prob. 2YTCh. 11.1 - Prob. 3YTCh. 11.1 - YOUR TURN In Example 6, find the goat population...Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Prob. 2ECh. 11.1 - Find the general solution for each differential...Ch. 11.1 - Prob. 4ECh. 11.1 - Prob. 5ECh. 11.1 - Prob. 6E
Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Prob. 10ECh. 11.1 - Find the general solution for each differential...Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Prob. 20ECh. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Find the particular solution for each initial...Ch. 11.1 - Prob. 35ECh. 11.1 - Prob. 36ECh. 11.1 - Prob. 37ECh. 11.1 - Prob. 38ECh. 11.1 - Prob. 39ECh. 11.1 - Prob. 40ECh. 11.1 - Suppose that 0y0N. Let b=(Ny0)y0, and let...Ch. 11.1 - Prob. 42ECh. 11.1 - Tracer Dye The amount of a tracer dye injected...Ch. 11.1 - Soil Moisture The evapotranspiration index I is a...Ch. 11.1 - Fish Population An Isolated fish population is...Ch. 11.1 - Dieting A persons weight depends both on the daily...Ch. 11.1 - Refer to Exercise 46. Suppose someone initially...Ch. 11.1 - U.S. Hispanic Population A recent report by the...Ch. 11.1 - U.S Asian Population Refer to Exercise 50. The...Ch. 11.1 - Guernsey Growth The growth of Guernsey cows can be...Ch. 11.1 - Flea Beetles A study of flea beetles found that...Ch. 11.1 - Plant Growth Researchers have found that the...Ch. 11.1 - Spread of a Rumor Suppose the rate at which a...Ch. 11.1 - Radioactive Decay The amount of a radioactive...Ch. 11.1 - Newtons Law of Cooling Newtons law of cooling...Ch. 11.1 - According to the solution in Exercise 58 of the...Ch. 11.1 - Newtons Law of Cooling When a dead body is...Ch. 11.1 - Prob. 61ECh. 11.2 - Prob. 1YTCh. 11.2 - YOUR TURN Solve the initial value problem...Ch. 11.2 - Prob. 1ECh. 11.2 - Prob. 2ECh. 11.2 - EXERCISES Find the general solution for each...Ch. 11.2 - EXERCISES Find the general solution for each...Ch. 11.2 - EXERCISES Find the general solution for each...Ch. 11.2 - EXERCISES Find the general solution for each...Ch. 11.2 - EXERCISES Find the general solution for each...Ch. 11.2 - EXERCISES Find the general solution for each...Ch. 11.2 - EXERCISES Find the general solution for each...Ch. 11.2 - Prob. 10ECh. 11.2 - EXERCISES Find the general solution for each...Ch. 11.2 - Prob. 12ECh. 11.2 - Prob. 13ECh. 11.2 - Prob. 14ECh. 11.2 - EXERCISES Solve each differential equation,...Ch. 11.2 - EXERCISES Solve each differential equation,...Ch. 11.2 - EXERCISES Solve each differential equation,...Ch. 11.2 - EXERCISES Solve each differential equation,...Ch. 11.2 - EXERCISES Solve each differential equation,...Ch. 11.2 - EXERCISES Solve each differential equation,...Ch. 11.2 - Prob. 21ECh. 11.2 - Prob. 22ECh. 11.2 - Prob. 24ECh. 11.2 - Prob. 29ECh. 11.2 - Prob. 30ECh. 11.2 - Prob. 31ECh. 11.2 - Prob. 32ECh. 11.2 - Prob. 33ECh. 11.3 - Use Eulers method to approximate the solution of...Ch. 11.3 - Prob. 1ECh. 11.3 - Prob. 2ECh. 11.3 - Prob. 3ECh. 11.3 - Prob. 4ECh. 11.3 - Use Eulers method to approximate the indicated...Ch. 11.3 - Prob. 6ECh. 11.3 - Use Eulers method to approximate the indicated...Ch. 11.3 - Prob. 8ECh. 11.3 - Prob. 9ECh. 11.3 - Prob. 10ECh. 11.3 - Use Eulers method to approximate the indicated...Ch. 11.3 - Use Eulers method to approximate the indicated...Ch. 11.3 - Use Eulers method to approximate the indicated...Ch. 11.3 - Use Eulers method to approximate the indicated...Ch. 11.3 - Use Eulers method to approximate the indicated...Ch. 11.3 - Prob. 16ECh. 11.3 - Use Eulers method to approximate the indicated...Ch. 11.3 - Use Eulers method to approximate the indicated...Ch. 11.3 - Prob. 19ECh. 11.3 - Prob. 20ECh. 11.3 - Prob. 21ECh. 11.3 - Prob. 22ECh. 11.3 - Solve each differential equation and graph the...Ch. 11.3 - Prob. 28ECh. 11.3 - Prob. 29ECh. 11.3 - Prob. 31ECh. 11.3 - Immigration An island is colonized by immigration...Ch. 11.3 - Insect Population A population of insects y,...Ch. 11.3 - Whale Population Under certain conditions a...Ch. 11.3 - Goat Growth The growth of male Saanen goats can be...Ch. 11.3 - Spread of Rumors A rumor spreads through a...Ch. 11.4 - For Exercises 1-8, solve the system of...Ch. 11.4 - For Exercise 1-8, solve the system of differential...Ch. 11.4 - For Exercises 1-8, solve the system of...Ch. 11.4 - For Exercises 1-8, solve the system of...Ch. 11.4 - For Exercises 1-8, solve the system of...Ch. 11.4 - For Exercises 1-8, solve the system of...Ch. 11.4 - For Exercise 9-14, find the particular solution...Ch. 11.4 - Prob. 10ECh. 11.4 - Prob. 11ECh. 11.4 - Prob. 12ECh. 11.4 - For Exercise 9-14, find the particular solution...Ch. 11.5 - YOUR TURN Consider the system of differential...Ch. 11.5 - YOUR TURN Letting p=4,q=1,r=3,ands=5 in Example 2,...Ch. 11.5 - Prob. 9ECh. 11.5 - Whales and Krill For the system of differential...Ch. 11.5 - Prob. 12ECh. 11.5 - Prob. 13ECh. 11.5 - Prob. 17ECh. 11.5 - Prob. 18ECh. 11.6 - YOUR TURN 1 Suppose that an epidemic in a...Ch. 11.6 - Prob. 2YTCh. 11.6 - Spread of an Epidemic The native Hawaiians lived...Ch. 11.6 - Prob. 3ECh. 11.6 - Prob. 4ECh. 11.6 - Prob. 5ECh. 11.6 - Prob. 6ECh. 11.6 - Prob. 7ECh. 11.6 - Prob. 8ECh. 11.6 - Solve Exercise 10 if pure water is added instead...Ch. 11.6 - Prob. 14ECh. 11.6 - Solve Exercise 14 if a 25 solution of the same...Ch. 11.6 - Prob. 16ECh. 11.CR - Prob. 1CRCh. 11.CR - Prob. 2CRCh. 11.CR - Prob. 3CRCh. 11.CR - Prob. 4CRCh. 11.CR - Prob. 5CRCh. 11.CR - Prob. 6CRCh. 11.CR - Prob. 7CRCh. 11.CR - Prob. 8CRCh. 11.CR - Prob. 9CRCh. 11.CR - Prob. 10CRCh. 11.CR - Prob. 11CRCh. 11.CR - Prob. 12CRCh. 11.CR - Prob. 13CRCh. 11.CR - Prob. 14CRCh. 11.CR - Prob. 15CRCh. 11.CR - Prob. 16CRCh. 11.CR - Prob. 17CRCh. 11.CR - Prob. 18CRCh. 11.CR - Prob. 19CRCh. 11.CR - Classify each equation as separable, linear, both...Ch. 11.CR - Prob. 21CRCh. 11.CR - Prob. 22CRCh. 11.CR - Prob. 23CRCh. 11.CR - Prob. 24CRCh. 11.CR - Prob. 25CRCh. 11.CR - Prob. 26CRCh. 11.CR - Prob. 27CRCh. 11.CR - Prob. 28CRCh. 11.CR - Prob. 29CRCh. 11.CR - Prob. 30CRCh. 11.CR - Prob. 31CRCh. 11.CR - Prob. 32CRCh. 11.CR - Prob. 33CRCh. 11.CR - Prob. 34CRCh. 11.CR - Prob. 35CRCh. 11.CR - Prob. 36CRCh. 11.CR - Prob. 37CRCh. 11.CR - Prob. 38CRCh. 11.CR - Prob. 39CRCh. 11.CR - Prob. 40CRCh. 11.CR - Prob. 41CRCh. 11.CR - Prob. 42CRCh. 11.CR - Prob. 43CRCh. 11.CR - Prob. 44CRCh. 11.CR - Prob. 45CRCh. 11.CR - Prob. 46CRCh. 11.CR - Prob. 47CRCh. 11.CR - Prob. 48CRCh. 11.CR - Prob. 49CRCh. 11.CR - Prob. 50CRCh. 11.CR - Prob. 51CRCh. 11.CR - Prob. 52CRCh. 11.CR - Solve each of the following systems of...Ch. 11.CR - Prob. 54CRCh. 11.CR - Effect of Insecticide After use of an experimental...Ch. 11.CR - Growth of a Mite Population A population of mites...Ch. 11.CR - Prob. 60CRCh. 11.CR - Prob. 61CRCh. 11.CR - Prob. 68CRCh. 11.CR - Prob. 69CRCh. 11.CR - Prob. 70CRCh. 11.CR - Prob. 71CRCh. 11.EA - Prob. 1EACh. 11.EA - Prob. 2EACh. 11.EA - Prob. 3EACh. 11.EA - Prob. 5EACh. 11.EA - Prob. 7EACh. 11.EA - Prob. 8EA
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