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Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

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Chapter
Section
BuyFindarrow_forward

Finite Mathematics and Applied Cal...

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

Sales OHaganBooks.com modeled its weekly sales over a period of time with the function

s ( t ) = 6 , 050 + 4 , 470 1 + 14 ( 1.73 t ) , as shown in the following graph (t is measured in weeks):

images

a. As time goes on, it appears that weekly sales are leveling off. At what value are they leveling off?

b. When did weekly sales rise above 10,000?

c. When, to the nearest week, were sales rising most rapidly?

(a)

To determine

To calculate: The weekly sales at which the sales get levelled off as the time increases if the weekly sales of OHaganBooks.com over a period of time t is given by the function,

s(t)=6,050+4,4701+14(1.73)t

The graph representing the weekly sales of OHaganBooks.com with the time in weeks is as follows,

images

Explanation

Given Information:

The weekly sales of OHaganBooks.com over a period of time t is given by the function,

s(t)=6,050+4,4701+14(1.73)t

The graph representing the weekly sales of OHaganBooks.com with the time in weeks is as follows,

Formula used:

The logistic function f(x) is of the form,

f(x)=N1+Abx

Where, N, A and b are constants such that A and b are positive and b is not equal to 1.

The value of N is called as limiting value of logistic curve y=N1+Abx where the value of y becomes equal to N.

Calculation:

Consider that the weekly sales of OHaganBooks

(b)

To determine

To calculate: The time required to reach the sales above 10,000 if the weekly sales of OHaganBooks.com over a period of time t is given by the function,

s(t)=6,050+4,4701+14(1.73)t

The graph representing the weekly sales of OHaganBooks.com with the time in weeks is as follows,

images

(c)

To determine

To calculate: The time to the nearest week at which the sales were rising more quickly if the weekly sales of OHaganBooks.com over a period of time t is given by the function,

s(t)=6,050+4,4701+14(1.73)t

The graph representing the weekly sales of OHaganBooks.com with the time in weeks is as follows,

images

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