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Mathematical Applications for the ...

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

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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)=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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Sect-13.1 P-9ESect-13.1 P-10ESect-13.1 P-11ESect-13.1 P-12ESect-13.1 P-13ESect-13.1 P-14ESect-13.1 P-15ESect-13.1 P-16ESect-13.1 P-17ESect-13.1 P-18ESect-13.1 P-19ESect-13.1 P-20ESect-13.1 P-21ESect-13.1 P-22ESect-13.1 P-23ESect-13.1 P-24ESect-13.1 P-25ESect-13.1 P-26ESect-13.1 P-27ESect-13.1 P-28ESect-13.1 P-29ESect-13.1 P-30ESect-13.1 P-31ESect-13.1 P-32ESect-13.1 P-33ESect-13.1 P-34ESect-13.1 P-35ESect-13.1 P-36ESect-13.1 P-37ESect-13.1 P-38ESect-13.1 P-39ESect-13.1 P-40ESect-13.2 P-1CPSect-13.2 P-2CPSect-13.2 P-1ESect-13.2 P-2ESect-13.2 P-3ESect-13.2 P-4ESect-13.2 P-5ESect-13.2 P-6ESect-13.2 P-9ESect-13.2 P-10ESect-13.2 P-11ESect-13.2 P-12ESect-13.2 P-7ESect-13.2 P-8ESect-13.2 P-23ESect-13.2 P-24ESect-13.2 P-13ESect-13.2 P-14ESect-13.2 P-15ESect-13.2 P-16ESect-13.2 P-17ESect-13.2 P-18ESect-13.2 P-19ESect-13.2 P-20ESect-13.2 P-21ESect-13.2 P-22ESect-13.2 P-25ESect-13.2 P-26ESect-13.2 P-27ESect-13.2 P-28ESect-13.2 P-29ESect-13.2 P-30ESect-13.2 P-31ESect-13.2 P-32ESect-13.2 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