# 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!
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%
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.