CK-12-Calculus

6.4. Exponential Growth and Decay http://www.ck12.org

MEDIA

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URL: http://www.ck12.org/flx/render/embeddedobject/586

For a video presentation of exponential decay(14.0), see Just Math Tutoring, Exponential Decay, Finding Half-Life
(6:08).

MEDIA

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URL: http://www.ck12.org/flx/render/embeddedobject/587

For additional problems on exponential growth and decay(14.0), see Khan Academy, Word Problem Solving, Expo
nential Growth and Decay (7:21).

MEDIA

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URL: http://www.ck12.org/flx/render/embeddedobject/114

Review Questions

1. In 1990, the population of the USA was 249 million. Assume that the annual growth rate is 1.8%.
   a. According to this model, what was the population in the year 2000?
   b. According to this model, in which year will the population reach 1 billion?


2. Prove that if a quantityAis exponentially growing and ifA 1 is the value att 1 andA 2 at timet 2 ,then the growth
   rate will be given by

k=t 1 −^1 t 2 ln

(A 1

A 2

)

.

3. Newton’s Law of Cooling states that the rate of cooling is proportional to the difference in temperature between
   the object and the surroundings. The law is expressed by the formulaT(t) = (T 0 −Tr)e−kt+TrwhereT 0 is the
   initial temperature of the object att= 0 ,Tris the room temperature (the surroundings), andkis a constant that
   is unique for the measuring instrument (the thermometer) called thetime constant.Suppose a liter of juice at
   23 ◦Cis placed in the refrigerator to cool. If the temperature of the refrigerator is kept at 11◦Candk= 0. 417 ,
   what is the temperature of the juice after 3 minutes?


4. Referring back to problem 3, if it takes an object 320 seconds to cool from 40◦Cabove room temperature to
   22 ◦Cabove room temperature, how long will it take to cool another 10◦Cafter it reaches 22◦Cabove room
   temperature?