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Math
Mathematical Applications for the Management, Life, and Social Sciences11th Edition

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Chapter 13.6, Problem 36E
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Mathematical Applications for the ...

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

Solutions

Chapter
Section
Problem 1CP
Problem 2CP
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
BuyFindarrow_forward

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)=100te−0.1t.

Explanation

Given Information:

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

f(t)=100te−0.1t.

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=uv−∫vdu

Calculation:

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

f(t)=100te−0.1t

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 100te−0.1t in above equation to obtain total income as,

TI=∫010100te−0.1tdt

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

u=t

And,

dv=e−0

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