   Chapter 13.4, Problem 4E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Suppose that the Quick-Fix Car Service franchise finds that the income generated by its stores can be modeled by assuming that the income is a continuous stream with a monthly rate of flow at time t given by f ( t )   =  10 .000 e 0.02 t (dollars per month)Find the total income from a Quick-Fix store for the first 2 years of operation.

To determine

To calculate: The total income from a Quick-Fix store for the first 2 year for monthly rate of flow by f(t)=10000e0.02t dollars per month, where, t is the time in months.

Explanation

Given Information:

The monthly rate of flow f(t)=10000e0.02t dollars per month.

Where, t is the time in months.

Formula used:

According to the total income of a Continuous Income Stream:

If the rate of receipt of revenue is f(t) dollars per unit of time, then the total income received for k year time is,

Total income=0kf(t)dt

Calculation:

Consider the provided function,

f(t)=10000e0.02t

Since, the income to be calculated for 24 months.

So, the value of k is,

k=24

Consider the formula,

Total income=0kf(t)dt

Substituting 24 for k and 10000e0.02t for f(t) to get:

Total income=024(10000e0

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