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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Capital Campaign The board of trustees of a college is planning a five-year capital gifts campaign to raise money for the college. The goal is to have an annual gift income I that is modeled by

I   = 2 0 0 0 ( 3 7 5   +       68 t e 02 t ) , o t 5 where t is the time in years.

(a) Use a graphing utility to decide whether the board of trustees expects the gift income to increase or decrease over the five-year period.

(b) Find the expected total gift income over the five- year period.

(c) Determine the average annual gift income over the five-year period.

(a)

To determine

Whether the board of trustees expects the gift income to increase or decrease over the period of 5 years by using graphing utility when they are planning a five-year capital gift campaign to raise fund for the college and the aim is to have an annual gift income I which is modelled by the function,

I=2000(375+68te0.2t),   0t5 

Where t is the time in years.

Explanation

Given Information:

The board of trustees are planning a five-year capital gift campaign to raise fund for the college and the aim is to have an annual gift income I which is modelled by the function,

I=2000(375+68te0.2t),   0t5 

Where t is the time in years.

Consider the function,

I=2000(375+68te0.2t),   0t5 

Now use TI-83 graphing calculator to obtain the graph by following the provided steps as,

Step 1: Press the [WINDOW] key and set the window as,

Xmin=0Xmax=5X scl=1Ymin=

(b)

To determine

To calculate: The expected total gift income over the period of five-years when the board of trustees are planning a five-year capital gift campaign to raise fund for the college and the aim is to have an annual gift income I which is modelled by the function,

I=2000(375+68te0.2t),   0t5 

Where t is the time in years.

(c)

To determine

To calculate: The average annual gift income over the period of five years the board of trustees are planning a five-year capital gift campaign to raise fund for the college and the aim is to have an annual gift income I which is modelled by the function,

I=2000(375+68te0.2t),   0t5 

Where t is the time in years.

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