   Chapter 13.6, Problem 36E ### 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

# Income streams Suppose the income from an Internet access business is a continuous income stream with annual rate of flow given by f ( t ) = 100 t e − 0.1 t in thousands of dollars per year. Find the total income over the next 10 years.

To determine

To calculate: The total income over the next 10 years if a continuous income stream with annual rate of flow is given by f(t)=100te0.1t.

Explanation

Given Information:

A continuous income stream with annual rate of flow is given by,

f(t)=100te0.1t.

Formula used:

The total income for a continuous income stream f(t) over a course of T years is given by,

TI=0Tf(t)dt

The formula for integration by parts is given by:

udv=uvvdu

Calculation:

As it is provided that a continuous income stream with annual rate of flow is given by,

f(t)=100te0.1t

Now, the total income for a continuous income stream f(t) over a course of T years is given by,

TI=0Tf(t)dt

Since, the total income is to be obtained over 10 years, so substitute 10 for T and 100te0.1t in above equation to obtain total income as,

TI=010100te0.1tdt

Now, use the method of integration by parts by splitting the integrands into two components, thus,

u=t

And,

dv=e0

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