   Chapter 4.6, Problem 10E ### 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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# Determining Exponential Growth and Decay In Exercises 7–10, use the given information to write an exponential equation for y. Does the function represent exponential growth or exponential decay? d y d t = 5.2 y ,       y = 18     when     t = 0

To determine

The exponential equation for y if dydt=5.2y,y=18when t=0 and identify whether the function is exponential growth or decay.

Explanation

Given Information:

The provided information is dydt=5.2y,y=18when t=0.

Consider the definition:

If the rate of change of a positive quantity y with respect to time is proportional to the amount of quantity present at any time t, that is dydt=ky, then y is given by the equation, y=Cekt, where C is the value of the quantity at time t=0 and k is the constant of proportionality.

If k>0 then there is exponential growth and when k<0 then there is exponential decay.

Now, consider the provided information is dydt=5

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