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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Present Value A company expects its income c during the next 4 years to be modeled by

c = 200 , 000 + 50 , 000 t , 0 t 4.

(a) Find the actual income for the business over the 4 years.

(b) Assuming an annual inflation rate of 6%, what is the present value of this income?

(a)

To determine

To calculate: The actual income of a company for a time period of 4 years if c be its expected income which is given as, c=200,000+50,000t where, 0t4.

Explanation

Given Information:

The expected income, c, is 200,000+50,000t and the time period is 4 years.

Formula used:

The expression for the actual income over a time period of t1 is,

Actual income=0t1c(t)dt

Here, c(t) represents the income which is a function of time t.

The method of integration by parts for two differentiable function of x, u and v is,

udv=uvvdu

Calculation:

Consider the expected income function, c=200,000+50,000t.

Since the time period is 4 years

(b)

To determine

To calculate: The present value of income c=200,000+50,000t of a company for a time period of 4 years, if the actual inflation rate of 6%.

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