7.1-2 Homework: Exponential Models
Name: _______________
Tell whether the function represents exponential growth or decay.
5
1. f ( x)  3  
7
x
4. f ( x)  0.25(1.05) x
1 7
2. f ( x)   
3 5 
5. f ( x)  3e x
x
3. f ( x)  3(4) x
1
6. f ( x)  e x
3
Graph the function. Tell the domain and the range of the function.
1
5
7 y  2( ) x  3
1
9. f ( x)  (5) x 3
2
1
2
8. y  e x
1
10. y  2  5  
 3
x
11. You deposit $1800 in a bank account for 5 years at an annual rate of 4.5%. Find the balance
in the account if it is compounded
a. Monthly
b. Daily
c. Weekly
12. You drink a beverage with 120 milligrams of caffeine. Each hour h, the amount of caffeine
c, in your system decreases by about 12%. Write an exponential model that describes the
situation. How many mg of caffeine are in your system in 3 hours?
13. In 2009, there were 1570 bears in a wildlife refuge. In 2010, the population
had increased to approximately 1884 bears. If this trend continues and the bear
population is increasing exponentially, how many bears will there be in 2017?
14. The value of a piece of equipment has a decay factor of 0.80 per year. After
5 years, the equipment is worth $98,304. What was the original value of
the equipment?
15. Your friend drops a rubber ball from 4 ft. You notice that its rebound is 32.5 in.
on the first bounce and 22 in. on the second bounce.
a. What exponential function would be a good model for the height of the
ball?
b. How high will the ball bounce on the fourth bounce?
16. An investment of $75,000 increases at a rate of 12.5% per year. What is
the value of the investment after 30 years?
17. A new truck that sells for $29,000 depreciates 12% each year. What is the
value of the truck after 7 years?
18. The price of a new home is $350,000. The value of the home appreciates 2%
each year. How much will the home be worth in 10 years?
19. In 1965 the federal debt of the United States was $322.3 billion. During the next 30 years,
the debt increased by about 10.2% each year.
a. Write a model giving the amount D (in billions of dollars) of debt t years after 1965. About
how much was the federal debt in 1980?
b. Estimate the year when the federal debt was $2,120 billion.
20. Find the amount in a continuously compounded account if $20,000 is invested at 3.75%
annual interest for 8 years.
21. How long would it take to double your principal at an annual interest
rate of 7% compounded continuously?
22. The isotope Hg-197 is used in kidney scans. It has a half-life of
64.128 h. After that time, half the isotope will have decayed. Write
the exponential decay function for a 12-mg sample. Find the amount
remaining after 72 h.
23. The isotope Sr-85 is used in bone scans. It has a half-life of 64.9 days.
Write the exponential decay function for an 8-mg sample. Find the amount
remaining after 100 days.
24. Suppose you invest $2000 at an annual interest of 5.5%
compounded continuously.
a. How much will you have in the account in 10 years?
b. How long will it take for the account to reach $5000?
25. You deposit $10,000 into a bank account that earns 5.2% annual interest for 5 years. What is
the balance if the interest is compounded
a. Quarterly
b. Continuously
26. Use your calculator to figure out about how many years it would take $100 to double, if it
were compounded continuously, at a 6% annual interest rate?
1. If your great-grandmother deposited $50 in a bank account in 1927, and it earned 3.5% annual
interest compounded continuously, what is the current balance?
2. In 1990 the population of Winnemucca, Nevada was 6191. The population increases 4% each
year. What is the population now?