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Math
CalculusSingle Variable Calculus: Early Transcendentals, Volume I8th Edition

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Chapter 3.9, Problem 40E
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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Brain weight B as a function of body weight Win fish has been modeled by the power function B = 0.007W2/3, where R and W are measured in grams. A model for body weight as a function of body length L. (measured in centimeters) is W = 0.12L2.53. If, over 10 million years, the average length of a certain species of fish evolved from 15 cm to 20 cm at a constant rate, how fast was this species' brain growing when the average length was 18 cm?

To determine

To find: The rate of change of brain of the given species when the average length is 18 cm.

Explanation

Given:

The brain weight B and the body weight W modeled by the power function B=0.007W23, where B and W are measures in gram.

The another model for body weight W is the function of body length L (in centimeter) given by the equation W=0.12L2 .  53.

Formula used:

(1) Chain rule: dydx=dydu⋅dudx

Calculation:

Since the average length changes with the time t .

Therefore, the body weight and brain weight, becomes also changes with time t.

That is average length, body weight and brain weight are the function of the time t.

Since average change in length is dLdt=20−1510000000  cm/yr.

Find dBdt when the average length is 18 cm.

Now by using chain rule

dBdt=dBdW⋅dWdL⋅dLdt

By using B=0.007W23 and W=0.12L2 .  53 in above.

dBdt=ddW[0.007W23]ddL[0.12L2 .  53]dLdt=(0.007)(23W - 13)(0.12)(2.53L1.53)(20-1510000000)

Substitutes W=0.12L2 .  53 and in dBdt

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Chapter 3.9,
Problem 39E
Chapter 3.9,
Problem 41E
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