   Chapter 6.2, Problem 8QY ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# A small business expects its income c during the next 7 years to be given by c ( t ) = 32 , 000 t , ≤ t ≤ 7 .(a) Find the actual income for the business over the 7 years.(b) Assuming an annual inflation rate of 3.3 % , what is the present value of this income?

(a)

To determine

To calculate: The actual income for business over next 7 years, when income of business is modelled as x=32000t for 0t7.

Explanation

Given Information:

The income of business is modelled as x=32000t for 0t7.

Formula used:

General Power Rule of Integration,

undu=un+1n+1+C

Here, n is the any number.

Calculation:

Consider the provided expression,

x=32000t

Integrate the above function from lower limit as 0 and higher limit as 7 in order to find the actual income for business over next 7 years.

x=0732000tdt=3200007tdt

Use the formula for general power rule of integration to solve above integration

(b)

To determine

To calculate: The present value of income for business over next 7 years, when income of business is modelled as x=32000t for 0t7 and annual rate of inflation is 3.3%.

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