   Chapter 13.4, Problem 3E ### 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

# Suppose that a steel company views the production of its continuous caster as a continuous income stream with a monthly rate of flow at time t given by f ( t )   =   24 , 000 e 0.03 t (dollars per month)Find the total income from this caster in the first year.

To determine

To calculate: The total income from the caster in the first year for monthly rate of flow f(t)=24000e0.03t dollars per month, where, t is the time in months.

Explanation

Given Information:

The monthly rate of flow f(t)=24000e0.03t dollars per month,

Where, t is the time in months.

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)=24000e0.03t

Since, the income to be calculated for 12 months.

So, the value of k is,

k=12

Consider the formula,

Total income=0kf(t)dt

Substituting 12 for k and 24000e0.03t for f(t) to get:

Total income=012(24000e0

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