   Chapter 2.8, Problem 38E ### 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

# Water temperature affects the growth rate of brook trout. The table shows the amount of weight gained by brook trout after 24 days in various water temperatures. Temperature(°C) 15.5 17.7 20.0 22.4 24.4 Weight gained (g) 37.2 31.0 19.8 9.7 -9.8 If W(x) is the weight gain at temperature x, construct a table of estimated values for W' and sketch its graph. What are the units for W'(x)?

To determine

To construct: The table of estimated values of W and sketch its graph.

Explanation

Given:

The table represents the weight gained at temperature x.

Formula used: For small h,

limh0W(x+h)W(x)hW(x+h)W(x)h

Calculation:

Calculation of W(15.5) is as follows,

Substitute h=2.2 in the formula

W(15.5)=W(15.5+2.2)W(15.5)2.2=W(17.7)W(15.5)2.2=3137.22.2=2.82

Thus, W(15.5)=2.82.

Calculation of W(17.7) is as follows,

Substitute h=2.2 in the formula

W(17.7)=W(17.72.2)W(17.7)2.2=W(15.5)W(17.7)2.2=37.2312.2=2.82

Substitute h=2.3 in the formula

W(17.7)=W(17.7+2.3)W(17.7)2.3=W(20)W(17.7)2.3=19.8312.3=4.87

Take the average of above two calculations of W(17.7)

W(17.7)=12(2.824.87)=3.845

Thus, W(17.7)=3.845.

Calculation of W(20) is as follows,

Substitute h=2.3 in the formula,

W(20)=W(202.3)W(20)2.3=W(17.7)W(20)2.3=3119.82.3=4.87

Substitute h=2.4 in the formula,

W(20)=W(20+2.4)W(20)2.4=W(22

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 