Exponential Word Problems
A  A0 b 
t
k
• What do each of the variables stand for?
• When do we use this equation? What are
some of the key words?
Examples
1) 200kg of Uranium is stored in a nuclear waste
facility. If the half-life of Uranium is 2000 years,
how much Uranium will remain radioactive after
500 years? 10000 years?
2) A certain bacteria reproduces in a such a way that
it doubles its population every 4 hours. If 250 are
present now, how many bacteria will there be in 3
hours? 6 hours?
A  P 1  r 
t
• What do the variables stand for?
• When do we use this equation? What are
some of the key words?
Examples
1) On average, colleges and universities in the U.S. have raised
tuition by 6.3% a year since 1958 (www.finaid.com). If the cost to
attend ____________ is _____________ per year now, how much
will it be to send your kids in 28 years? How much would it have
cost your parents to attend the same university 24 years ago?
***Sample tuitions at present (www.collegeboard.com)
University of Pennsylvania $36,000
Penn State University $13,000 (in-state)
Millersville $8,000 (in-state)
Notre Dame $35,000
University of Virginia $25,000
3) The rate at which caffeine is eliminated from the
bloodstream of an adult is 15% of the original amount
per hour. An adult drinks a soda and the caffeine
reaches a peak level of 30 milligrams. Predict how much
will remain in his body after 1 hour? 4 hours?
 r
A  P 1  
 n
nt
• What do each of the variables stand for?
• When do we use this equation? What are
some of the key words?
Examples
1)
When John was 8 years old his grandparents gave him
a $2,000 investment. The investment is in a mutual
fund that earns 8% interest compounded quarterly.
How much will the investment be worth when John
goes to college at age 18? How much would the
investment be worth when John retires at age 65?
2)
A couple inherits $20,000 and they decide to invest it
to pay for their child’s education. If the money is
invested in an account that pays 7% interest
compounded monthly, how much will they have when
their child goes to college in 20 years?
A  Pe
rt
• What do each of the variables stand for?
• When do we use this equation? What are
the key words?
Examples
1)
A person charges $5,000 on a credit card that charges
18.99% interest compounded continuously. How
much will the person owe (not including late charges) if
he does not pay back the loan for 3 years?
2)
A man takes out a loan for $10,000 that charges
6.99% interest compounded continuously. How much
will the man owe in 5 years?