   Chapter 13.4, Problem 6E ### 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

# A company that services a number of vending machines considers its income as a continuous stream with an annual rate of flow at time t given by f ( t )   = 120 e − 0.4 t in thousands of dollars per year. Find the income from this stream over the next 5 years.

To determine

To calculate: The total income of the company services a number of vending machines for next 5 year from continuous income stream which approximated by f(t)=120e0.4t thousands of dollars per year, where, t is the time in years.

Explanation

Given Information:

The total income of the company services a number of vending machines for next 5 year from continuous income stream is approximated by f(t)=120e0.4t thousands of dollars per year.

Where, t is the time in years.

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)=120e0.4t

Since, the income to be calculated for next 5 years.

So, the value of k is,

k=5

Consider the formula,

Total income=0kf(t)dt

Substituting 5 for k and 120e0.4t for f(t) to get:

Total income=05(120e0

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