   Chapter 2.2, Problem 23E 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 ) 100 200 400 600 800 g ( x ) 100 20 4 0.8 0.16

To determine

Whether the exponential function is formed by the function f(x) and g(x) from the following table,

 x −2 −1 0 1 2 f(x) 100 200 400 600 800 g(x) 100 20 4 0.8 0.16

If yes, then provide the exponential model.

Explanation

Given information:

The provided table is:

 x −2 −1 0 1 2 f(x) 100 200 400 600 800 g(x) 100 20 4 0.8 0.16

Consider the following data table,

 x −2 −1 0 1 2 f(x) 100 200 400 600 800 g(x) 100 20 4 0.8 0.16

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 2 till the value of x reaches the value of 0, after this the data does not follow the same pattern. This suggest that f(x) is not an exponential function fitting data.

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

Consider the formula of exponential function,

g(x)=Bcx

Substitute x=0 in the equation g(x)=Bcx,

g(0)=Bc0

From the table, g(0)=4 and c0=1

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