   Chapter 4.6, Problem 6E ### 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

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 (3,12) and (4,5).

Hence the points (3,12) and (4,5) satisfy the equation of exponential function y=Cekt.

Substitute t=3,y=12 in the equation y=Cekt.

12=Cek(3)12=Ce3k

Substitute t=4,y=5 in the equation y=Cekt.

5=Cek(4)5=Ce4k

Now take the ratio of the equations Ce3k=12 and Ce4k=5,

Ce4kCe3k=512e4ke3k=25e4k3k=10ek=10

Take natural logarithm of both the sides

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