   Chapter 13.4, Problem 2E ### 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

# Find the total income over the next 8 years from a continuous income stream with an annual rate of flow at time t given by f ( t ) =   8500 e − 0.2 t (dollars per year).

To determine

To calculate: The total income for next 8 years from continuous income stream for an annual rate of flow f(t)=8500e0.2t dollars per year, where, t is the time in years.

Explanation

Given Information:

The annual rate of flow is provided by the function f(t)=8500e0.2t 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)=8500e0.2t

Since, the income to be calculated for next 8 years.

So, the value of k is,

k=8

Consider the formula,

Total income=0kf(t)dt

Substituting 8 for k and 8500e0.2t for f(t) to get:

Total income=08(8500e0

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