   Chapter 13.3, Problem 42E ### 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

# Total income Suppose that the income from a slot machine in a casino flows continuously at a rate of f ( f )   =   100 e 0.1 t where t is the time in hours since the casino opened. Then the total income during the first 10 hours is given by ∫ 0 10 100 e 0.1 t   d t Find the average income over the first 10 hours.

To determine

To calculate: The average income over the first 10 hours where suppose that the income from a slot machine in a casino flows continuously at a rate of f(t)=100e0.1t, t is the time in hours since the casino opened and the total income during the first 10 hours is 010100e0.1tdt.

Explanation

Given information:

It is provided that suppose that the income from a slot machine in a casino flows continuously at a rate of f(t)=100e0.1t, t is the time in hours since the casino opened and the total income during the first 10 hours is 010100e0.1tdt.

Formula used:

Average value

The average value of a continuous function y=f(x) over the interval [a,b] is:

Average value=1baabf(x)dx

Calculation:

The provided function is:

f(t)=100e0.1t

Since, the average income over the first 10 hours is to be determined.

Thus, the interval is [0,10]

Consider the formula:

Average value=1baabf(x)dx

Substitute 10 for b, 0 for a and 100e0.1t for f(t) in above equation to get:

Average value=1100010(100e0

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