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Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

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BuyFindarrow_forward

Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Market Index Joe Downs runs a small investment company from his basement. Every week, he publishes a report on the success of his investments, including the progress of the Joe Downs Index. At the end of one particularly memorable week, he reported that the index for that week had the value I ( t ) = 1 , 000 + 1 , 500 t 800 t 2 + 100 t 3

points, where t represents the number of business days into the week; t ranges from 0 at the beginning of the week to 5 at the end of the week. The graph of I is shown below:

I(Joe Down Index)

images

On average, how fast and in which direction was the index changing over the first two business days (the interval [ 0 , 2 ]

)?[HINT: See Example 3.]

To determine

To calculate: The rate of change in index over the first two business days and its direction, if the index for a week has a value I(t)=1000+1500t800t2+100t3 and the graph of I is shown below.

images

Explanation

Given Information:

The function is I(t)=1000+1500t800t2+100t3 and the graph of I is shown below:

Formula used:

Average rate of change of f(x) over the interval [a,b] is:

Average rate of change of f=Change in fChange in x=ΔfΔx=f(b)f(a)ba

Calculation:

Consider the function I(t)=1000+1500t800t2+100t3,

From the graph shown below, find the value of index change in first two business day, that is in the interval [0,2].

Apply the average rate of change formula:

Average rate of change of I=I(2)I(0)20

Now, find I(2) and I(0):

Substitute the value 2 in the function I(t)=1000+1500t800t2+100t3:

I(2)=1000+1500(2)800(2)

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