Algebra 2 CP
7.1 – 7.2 (Day 2) Homework
Exponential Growth and
Decay Models Homework
Name__________________
Assignment D2
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.
10.
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.)____________________
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.
12.
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.)___________________
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
t
 1  5730
that remains in a sample after t years is given by this equation: P  100 
. What percent
 2
remains in a sample after
14.
a.
2500 years?
13a.)___________________
b.
5000 years?
13b.)___________________
c.
10000 years?
13c.)___________________
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.
16.
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.)___________________
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.
y  12191.12 where y represents the number of monk parakeets and t represents the number of years since 1992.
t
365t
.02 

2. A  8001 
 where A represents the amount in the account after t years.
365 

t
3. y  4501.06  where y represents the value of the table after t years.
4.
y  2000.75 where y represents the value of the bike after t years.
t
5.
y  5000.98 where y represents the value of the stock after t years.
6.
y  250000.85 where y represents the value of the car after t years.
t
7a. $1591.35
9b. $2406.98
t
7b. $1592.05
9c. $2383.23
13a. 73.9%
13b. 54.6%
15b. about 226
17. $108,483.93
7c. $1592.40
10. $1611.93
7d. $1592.64 7e. $1592.75 8. $313.75
9a. $2479.38
11a. $2804.71 11b. $2701.39 11c. $2666.99 12. 664,284
13c. 29.8%
14. V  13000.678
15c. about 317
18. 531,845
19. $102,168.90
t
15a. about 96
16. 11.6%
20. about 65 milligrams