Chapter 8.4, Problem 13E

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

Chapter
Section

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

# If the amount of capital that a company has at time t is f(t), then the derivative, f′(t), is called the net investment flow. Suppose that the net investment flow is t million dollars per year (where t is measured in years). Find the increase in capital (the capital formation) from the fourth year to the eighth year.

To determine

To calculate: The increase in capital from the fourth year to the eighth year.

Explanation

Given information:

The amount of capital at time t is f(t).

The net investment flow fâ€²(t)=t million dollars per year.

Calculation:

Apply Net change Theorem as follows:

The integral of a rate of change is the net change

âˆ«abFâ€²(x)dx=F(b)âˆ’F(a) (1)

Here, the lower limit is a and the upper limit is b.

Apply Net Change Theorem to calculate the increase in capital from the fourth year to the eighth year.

Modify Equation (1) for the calculation of capital.

âˆ«abfâ€²(t)dt=f(b)âˆ’f(a) (2)

Substitute 4 years for a, 8 years for b, and t million dollars per year for fâ€²(t)

Â in Equation (2)

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