3. Exponential Word Problems
• Compounded
Continuously
• Other compounds
• Half Life
• inc/decreasing and
app/depreciation
rt
PeA =
nt
n
r
PA )1( +=
halflife
x
inity
=
2
1
t
rinity )1( ±=
4. You have decided to invest $2500 at an 8% annual rate of
interest. How much will you have accumulated after 4 years
it is compounded:
– Annually?
– Quarterly?
– Daily?
– Continuously?
nt
n
r
PA )1( += nt
n
r
PA )1( +=
nt
n
r
PA )1( +=
5. You have decided to invest $10,000 at an 6.75% annual
rate of interest. How much will you have accumulated after
5 years it is compounded:
– Annually?
– Quarterly?
– Daily?
– Continuously?
nt
n
r
PA )1( += nt
n
r
PA )1( +=
nt
n
r
PA )1( +=
6. Suppose you invest $1050 at an annual interest rate of 5.5%
compounded continuously. How much will you have in the account
after 5 years?
Suppose you invest $1300 at an annual interest rate of 4.3%
compounded continuously. How much will you have in the
account after three years?
A = Pert
7. Interest
• An initial investment of $100 is now
valued at $149.18. The interest rate is
8% compounded continuously. How
long has the money been invested?
8. Another Example:
• Suppose a $125,000 piece of machinery is
depreciating at 8% every year.
– How much is it worth after 5 years?
– After 7 years?
– How long will it take for it to be worth less than $50,000?
9. How Long Problems?
• Suppose you buy a used car that costs
$11,800. The expected depreciation of the
car is 20% a year. When will the value be
$6,500?
10. How Long?
• The population of Ramsey City is currently
250 people with a growth rate of 9% a
year. How long until the population
reaches 5000 people?
11. Half Life Problem:
A hospital prepares a 100-mg supply of
technetium-99mg which has a half-life of 6
hours. Write an exponential function to find
the amount of technetium-99mg that remains
after 75 hours.
12. Another Half-Life:
• Arsenic-74 is used to locate brain tumors.
It has a half-life of 17.5 days. Write an
exponential decay function for a 90-mg
sample. Use the function to find the
amount remaining after 6 days.
13. How long?
• Ramsey-26 is a chemical that has a half-
life of 3 days. If Amy takes 300 mg of
Ramsey-26, then how much is left after 37
days? How long will it take for Amy to only
have 5 mgs left in her body?
