   Chapter 8.4, Problem 13E

Chapter
Section
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 f(t)=t million dollars per year.

Calculation:

Apply Net change Theorem as follows:

The integral of a rate of change is the net change

abF(x)dx=F(b)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.

abf(t)dt=f(b)f(a) (2)

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

in Equation (2)

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