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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

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

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