Ap Calculus Ab Junior Final Project
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Ap Calculus Ab Junior Final Project

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Student project lesson on exponential growth and decay for calculus or precalculus students

Student project lesson on exponential growth and decay for calculus or precalculus students

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Ap Calculus Ab Junior Final Project Ap Calculus Ab Junior Final Project Presentation Transcript

  • A P C a l c u l u s A B J u n i o r F i n a l P r o j e c t B y S h e l b y M o r r i s o n
  • 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=Ce kt
    • 14=3e k18
    • 4.667=e k18
    • 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=Ce kt
    • 12=10e k1
    • 1.2=e k1
    • ln(1.2)=k1
    • k=.18232
    • Y=10e 4(.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=Ce kt
    • 16=20e k2
    • .8=e k2
    • ln(.8)=k2
    • k= -.11157
    • Y=20e 6(-.11157)
    • Y=10.240 fleas left after 6 hours
  • Sources
    • Morrison, Shelby L. The Mind of Me . Fayetteville, AR: Morrison Inc., 2009.
  • The End