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By Shelby Morrison

Background Info

Michelle Johnson is the owner of a small, high-end doggy daycare in Fayetteville, Arkansas called Dogtown. After almost two years of running her business, Michelle’s clientele has grown significantly.

Exponential Growth

On the first day of opening her doggy daycare, Michelle watched only three dogs. However, after a year and a half Michelle now watches fourteen dogs everyday. At this rate, how long will it take Michelle to have twenty-four clients?

Exponential Growth Cont.

Y=Cekt

14=3ek18

4.667=ek18

ln(4.667)=k18

k=.08558

24=3e(.08558)t

8=e(.08558)t

ln(8)=.08558t

t=24.30 months until she has twenty-four clients

More Exponential Growth

Recently, Michelle discovered that one of the dogs that she watches, a sadistic Pomeranian named Bruiser, has fleas. At the time that Michelle discovered the fleas, she was able to count only ten. However, an hour later Michelle was able to find twelve fleas. If the fleas reproduced at a rate of 20% an hour, how many fleas were pestering Bruiser after four hours?

More Exponential Growth Cont.

Y=Cekt

12=10ek1

1.2=ek1

ln(1.2)=k1

k=.18232

Y=10e4(.18232)

Y=20.736 fleas after 4 hours

Rate of Decay

The day after finding fleas on Bruiser, Michelle noticed that a friendly German Shepherd named Twix had fleas too. She decided to take action quickly to reduce the risk of any further contamination so Michelle gave Twix a flea bath. Before applying the shampoo, Michelle counted twenty fleas on the dog. After two hours Michelle only found 16 fleas on Twix. At this rate, how many fleas will be left on Twix after six hours?

Rate of Decay Cont.

Y=Cekt

16=20ek2

.8=ek2

ln(.8)=k2

k= -.11157

Y=20e6(-.11157)

Y=10.240 fleas left after 6 hours

SourcesSources

Morrison, Shelby L. Morrison, Shelby L. The Mind of MeThe Mind of Me. . Fayetteville, AR: Morrison Inc., 2009.Fayetteville, AR: Morrison Inc., 2009.