Exponential Growth and Decay Word Problems

Exponential+Growth+and+Decay+Word+Problems
Name: Pd: Date:

  1. The!world!population!in!2000!was!approximately!6.08!billion.!The!
    annual!rate!of!increase!was!about!1.26%.
    a. Find!the!growth!factor!for!the!world!population.
    b. Suppose!the!rate!of!increase!continues!to!be!1.26%!. Write!a!
    function!to!model!the!world!population
    c. Let!x!be!the!number!of!years!past!the!year!2000.!Find!the!
    world!population!in!2010.
  2. A!computer!valued!at!$6500!depreciates!at!the!rate!of!14.3%!per!
    year.!
    a. Write!a!function!that!models!the!value!of!the!computer.
    b. Find!the!value!of!the!computer!after!three!years.
  3. The!population!of!a!certain!animal!species!decreases!at!a!rate!of!
    3.5%!per!year.!You!have!counted!80!of!the!animals!in!the!habitat!
    you!are!studying.
    a. Write!a!function!that!models!the!change!in the!animal!
    population.
    b. Graph!the!function.!Estimate!the!number!of!years!until!the!
    population!fist!drops!below!15!animals
    Exponential+Growth+and+Decay+Word+Problems
  4. Write!an!exponential!function!to!model!each!situation.!Find!the!
    value!of!each!function!after!five!years.
    a. A!$12,500!car!depreciates!9%!each!year
    b. A!baseball!card!bought!for!$50!increases!3%!in!value!each!
    year.
    5.+A!new!car!that!sells!for!$18,000!depreciates!25%!each!year.!Write!a
    function!that!models!the!value!of!the!car.!Find!the!value!of!the!car
    after!4!yr.
    6.+A!new!truck!that!sells!for!$29,000!depreciates!12%!each!year.!Write!a
    function!that!models!the!value!of!the!truck.!Find!the!value!of!the!truck
    after!7!yr.
    7.+The!bear!population!increases!at!a!rate!of!2%!per!year. There!are!
    1573 bear!this!year.!Write a!function!that!models!the!bear!population.!
    How many!bears!will!there!be!in!10!yr?
    Exponential+Growth+and+Decay+Word+Problems
    8.+An!investment!of!$75,000!increases!at!a!rate!of!12.5%!per!year.!Find!
    the value!of!the!investment!after!30!yr.
    9.+The!population!of!an!endangered!bird!is!decreasing!at!a!rate!of!0.75%
    per!year. There!are!currently!about!200,000!of!these!birds.!Write!a
    function!that!models!the!bird!population.!How!many!birds!will!there!be
    in!100!yr?
    Exponential+Growth+and+Decay+Word+Problems
    HalfVLife!Problems
  5. A!hospital!prepares!a!100mg!supply!of!technetiumV99m!which!has!
    a!halfVlife!of!6!hours.
    a. What!is!the!decay!factor?
    b. What!is!the!length of!a!halfVlife?
    c. Write!an!equation!to!represent!this!problem.
    d. Find!the!amount!of!technetiumV99m!that!remains!after!75!hours.
    2.!ArsenicV74!is!used!to!locate!brain!tumors.!It!has!a!halfVlife!of!17.5!
    days.
    a. What!is!the!decay!factor?
    e. What!is!the!length!of!a!halfVlife?
    b. Write!an!equation!to!represent!this!problem.
    c. Find!the!amount!remaining!after!6!days!from!a!90Vmg!sample.
  6. PhosphorusV32!is!used!to!study!a!plant’s!use!of!fertilizer.!It!has!a!
    halfVlife!of!14.3!days.!Write!the!exponential!decay!function!for!a!50V
    mg!sample.!Find!the!amount!of!phosporusV32!remaining!after!84!
    days.
    Exponential+Growth+and+Decay+Word+Problems
  7. IodineV131!is!used!to!find!leaks!in!water!pipes.!It!has!a!halfVlife!of!
    8.14!days.!Write!the!exponential!decay!function!for!a!200Vmg!
    sample.!Find!the!amount!of!IodineV131!remaining!after!72!days.
  8. CarbonV14!is!used!to!determine!the!age!of!artifacts!in!carbon!
    dating.!It!has!a!halfVlife!of!5730!years.!Write!the!function!for!a!24V
    mg!sample.!Find!the!amount!remaining!after!30!millennia!(1!
    millennium!=!1,000!years)
    6.!HgV197!is!used!in!kidney!scans.!It!has!a!halfVlife!of!64.128!h.!Write!the
    exponential!decay!function!for!a!12Vmg!sample.!Find!the!amount
    remaining!after!72!h.
    7.!SrV85!is!used!in!bone!scans.!It!has!a!halfVlife!of!64.9!days.!Write!the
    exponential!decay!function!for!an!8Vmg!sample.!Find!the!amount
    remaining!after!100!days.
    8.!IV123!is!used!in!thyroid!scans.!It!has!a!halfVlife!of!13.2!h.!Write!the
    exponential!decay!function!for!a!45Vmg!sample.!Find!the!amount
    remaining!after!5!h.

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