# The exponential function which is of the form f ( x ) = C b x for the given graph. ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 1.5, Problem 22E
To determine

## To find: The exponential function which is of the form f(x)=Cbx for the given graph.

Expert Solution

The equation of the graph is f(x)=2(23)x .

### Explanation of Solution

It is given that the equation of the given graph is of the form f(x)=Cbx .

Here, the graph represents a curve which passes through the points (−1, 3) and (1,43) .

Substitute these points in f(x)=Cbx ,

3=Cb1

3b=C (1).

43=Cb (2).

Substitute equation (1) in equation (2) and obtain the value of b as follows.

43=(3b)b4=9b2b2=49b=±23

Ignore the negative value of b as it cannot take the negative values.

Thus, the value of b=23 .

Substitute b=23 in equation (1) and obtain the value of C.

3(23)=CC=2

Therefore, the value of C = 2.

Substitute the value of b and C in f(x)=Cbx and obtain the required equation.

Therefore, the equation of the exponential function which passes through the points (−1,3) and (1,43) is f(x)=2(23)x .

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