# 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 21E
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)=3(2)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 (3, 24) and (1, 6).

Substitute these points in f(x)=Cbx ,

24=Cb3 (1)

6=Cb1 (2)

Divide the equation (1) by equation (2) and obtain the value of b as follows.

246=Cb3Cb14=b2b=±2

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

Thus, the value of b = 2.

Substitute b=2 in equation (1) and obtain the value of C.

24=C2324=8CC=3

Therefore, the value of C = 3.

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

Therefore, equation of the exponential function which passes through the points (3,24) and (1,6) is f(x)=3(2)x .

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