   Chapter 4.6, Problem 4E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Modeling Exponential Growth and Decay In Exercises 1-6, find the exponential function y = C e k t that passes through the two given points. y = C e k t To determine

To calculate: The exponential function y=Cekt for the following graph: Explanation

Given Information:

The provided graph is:

Consider the following graph:

Observe that the exponential function curve passes through the points (0,3) and (2,1).

Hence the points satisfy the equation of exponential function y=Cekt.

Substitute t=0,y=3 in the equation y=Cekt.

3=Cek(0)3=Ce03=C1C=3

Hence, the value of C is 3.

Substitute t=2,y=1 in the equation y=3ekt.

1=3ek(2)1=3e2k

Solve the equation 1=3e2k for k.

e2k=13

Taking natural logarithm of both the sides

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