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

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### 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=dydududx

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=201510000000cm/yr.

Find dBdt when the average length is 18 cm.

Now by using chain rule

dBdt=dBdWdWdLdLdt

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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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 