This document contains several word problems involving exponential and logarithmic functions related to investment, depreciation, population growth, and radioactive decay. It includes questions about calculating accumulated investment amounts over time compounded annually, quarterly, daily and continuously. It also includes problems about finding the value of depreciating assets or populations over time, as well as calculating the remaining amount of a radioactive substance after a given number of half-lives. The document provides the necessary formulas and concludes with assigning specific homework problems from the textbook and a worksheet.

1. Homework Questions

2. Word Problems with
Exponentials and Logs

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?

14. Homework
• Pg. 342 (3, 11, 17, 21-29 odd)
• Worksheet
• Sticker worksheet 