Algebra 2 CP Name______

7.1 – 7.2 (Day 2) Homework Assignment D5

Write an exponential model that describes the situation. Make sure to define all variables used.

1. In 1992, 1219 monk parakeets were observed in the United States. For the next 11 years, about

12% more parakeets were observed each year.

1.)______

2. You deposit $800 in an account that pays 2% annual interest compounded daily.

2.)______

3. You purchase an antique table for $450. The value of the table increases by 6% per year.


3.)______

4. You buy a new mountain bike for $200. The value of the bike decreases by 25% each year.

4.)______

5. You invest $500 in the stock of a company. The value of the stock decreases 2% each year.

5.)______

6. A new car costs $25000. The value of the car decreases 15% each year.

6.)______

Solve.

7. You deposit $1500 in a bank account that pays 3% annual interest. How much will you have in the

account after 2 years if the interest is compounded

a. yearly 7a.)______

b. semi-annually 7b.)______

c. quarterly 7c.)______

d. monthly 7d.)______

e. daily 7e.)______

8. You buy a new mountain bike for $450. The value of the bike decreases by 16.5% each year.

How much will the bike be worth in two years?

8.)______

9. You deposit $2200 in a bank account. Find the balance after four years for each of the situations

described:

a. The account pays 3% annual interest compounded quarterly. 9a.)______

b. The account pays 2.25% annual interest compounded monthly. 9b.)______

c. The account pays 2% annual interest compounded daily. 9c.)______

10. You buy a new computer for $2000. It depreciates at a rate of 5.25% per year. If you use it for

your four years of high school, how much will it be worth at the end of the four years?

10.)______

11. You are saving for your senior year spring break trip. You want to have $3000 in your savings account

after 3 years. Find the amount you should deposit for each of the situations described.

a. The account pays 2.25% annual interest compounded quarterly. 11a.)______

b. The account pays 3.5% annual interest compounded monthly. 11b.)______

c. The account pays 4% annual interest compounded yearly. 11c.)______

12. In 1990, the population of Austin, Texas was 494,290. During the next 10 years, the population

increased by about 3% each year. What was the population in 2000?

12.)______

13. When a plant or animal dies, it stops acquiring carbon-14 from the atmosphere. Carbon-14 decays

over time with a half-life of about 5730 years. The percent P of the original amount of carbon-14

that remains in a sample after t years is given by this equation: . What percent

remains in a sample after

a. 2500 years? 13a.)______

b. 5000 years? 13b.)______

c. 10000 years? 13c.)______

14. You buy a new stereo for $1300 and are able to sell it 4 years later for $275. Assume that the resale

value of the stereo decays exponentially with time. Write an equation giving the stereo’s resale value

V (in dollars) as a function of the time t (in years) since you bought it.

14.)______

15. In 1977, there were 41 breeding pairs of bald eagles in Maryland. Over the next 24 years, the

number increased by about 8.9% each year. About how many breeding pairs of bald eagles were

in Maryland in

a. 1987? 15a.)______

b. 1997? 15b.)______

c. 2001? 15c.)______

16. The yearly cost for residents to attend a state university has increased from $5200 to $9000 in the

last 5 years. To the nearest tenth of a percent, what has been the average annual growth rate

cost?

16.)______

17. The Martin’s bought a condominium for $85000. Assuming that the value of the condo will

appreciate about 5% per year, how much will the condo be worth in 5 years?

17.)______

18. In 1910, the population of a city was 120,000. Since then, the population has increased by

exactly 1.5% per year. If the population continues to grow at this rate, what will the population be

in 2010?

18.)______

19. A piece of machinery valued at $250,000 depreciates at a fixed rate of 12% per year. How much

will it be worth in 7 years?

19.)______

20. A cup of coffee contains 130 milligrams of caffeine. If caffeine is eliminated from the body at a rate

of 11% per hour, how much caffeine will be in the body after 6 hours (assuming no other caffeinated

drink was consumed)?

20.)______

ANSWERS

1. where y represents the number of monk parakeets and t represents the number of years since 1992.

2. where A represents the amount in the account after t years.

3. where y represents the value of the table after t years.

4. where y represents the value of the bike after t years.

5. where y represents the value of the stock after t years.

6. where y represents the value of the car after t years.

7a. $1591.35 7b. $1592.05 7c. $1592.40 7d. $1592.64 7e. $1592.75 8. $313.75 9a. $2479.38

9b. $2406.98 9c. $2383.23 10. $1611.93 11a. $2804.71 11b. $2701.39 11c. $2666.99 12. 664,284

13a. 73.9% 13b. 54.6% 13c. 29.8% 14. 15a. about 96

15b. about 226 15c. about 317 16. 11.6%

17. $108,483.93 18. 531,845 19. $102,168.90 20. about 65 milligrams