   Chapter 2.2, Problem 19E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

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

In Exercises 19-24 the values of two functions, f and g, are given in a table. One, both, or neither of them may be exponential. Decide which, if any, are exponential, and give the exponential models for those that are. [HINT: See Example 1.] x –2 –1 0 1 2 f ( x ) 0.5 1.5 4.5 13.5 40.5 g ( x ) 8 4 2 1 1 2

To determine

Which function in table is exponential, if there any exponential function then define its model also, table is shown below:

 x −2 −1 0 1 2 f(x) 0.5 1.5 4.5 13.5 40.5 g(x) 8 4 2 1 12
Explanation

Given information:

The provided table is:

 x −2 −1 0 1 2 f(x) 0.5 1.5 4.5 13.5 40.5 g(x) 8 4 2 1 12

Consider the following data table,

 x −2 −1 0 1 2 f(x) 0.5 1.5 4.5 13.5 40.5 g(x) 8 4 2 1 12

From the data table it can be observed that for every time value of x increases by 1, the value of f(x) is multiplied by 3

. This suggest that f(x) is an exponential function fitting data.

Use the formula of exponential function,

f(x)=Abx

Substitute x=0 in f(x)=Abx:

f(0)=Ab0 =A

Substitute f(0)=4.5 and b0=1

in f(0)=A:

4.5=A

Substitute x=1 in f(x)=Abx:

f(1)=Ab1

Substitute f(1)=13.5 and A=4.5

in f(1)=Ab1:

13.5=4.5b

Divide both side by 4.5.

13.54.5=4.5b4.5 3=bb=3

Thus, the exponential equation is f(x)=4.5(3)x.

From the data table it can also be observed that for every time value of x increases by 1, the value of g(x) is multiplied by 12

. This suggest that g(x) is an exponential function fitting data

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