   Chapter 2.2, Problem 62E 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 55-62, find an equation for an exponential function that passes through the pair of points given. (Round all coefficients to four decimal places when necessary] [HINT: See Example2.]Through ( − 1 ,     2 ) and ( 3 ,     1 )

To determine

To calculate: The equation for an exponential function that passes through the pair of points (1,2) and (3,1).

Explanation

Given Information:

The pair of points are (1,2) and (3,1).

Formula used:

Formula of exponential function is given by,

f(x)=Abx

Calculation:

Consider the following data table of the points (1,2) and (3,1),

 x −1 3 f(x) 2 1

Use the formula of exponential function,

f(x)=Abx

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

f(1)=Ab1

Substitute f(1)=2 in f(1)=Ab1:

2=Ab1

Substitute x=3 in f(x)=Abx:

f(3)=Ab3

Substitute f(3)=1 in f(3)=Ab3:

1=Ab3

Divide equation 1=Ab3 by 2=Ab1:

12=Ab3Ab1 12=b3b1 12=b4 b4=12

Take reciprocal power of both side:

b=(12)14

Substitute b=(12)14 in 2=A

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