Name:
Date:
Algebra II
Period:
8.1 – 8.3 Word Problems
Section 8.1 – Exponential Growth
When a real-life quantity increases by a fixed percent each year (or other time period), the amount y of the quantity
after t years can be modeled by:
1. The amount g (in trillions of cubic feet) of natural gas consumed in the United States from 1940 to 1970 can
be modeled by g = 2.91(1.07)t , where t is the number of years since 1940.
a. Identify the initial amount, the growth factor, and the annual percent increase.
b. Estimate the natural gas consumption in 1955.
2. In 1980 about 2,180,000 U.S. workers worked at home. During the next ten years, the number of workers
working at home increased 5% per year.
a. Write a model giving the number w (in millions) of workers working at home t years
after 1980.
b. Use the table feature in your calculator to estimate the year when there were about 3.22 million
workers who worked at home.
8.1 – 8.3 Word Problems: Pg. 1 of 5
Section 8.2 – Exponential Decay
When a real-life quantity decreases by a fixed percent each year (or other time period), the amount y of the
quantity after t years can be modeled by:
3. The number A (in millions) of record albums sold each year in the United States from 1982 to 1993 can be
modeled by A = 265(0.39)t, where t represents the number of years since 1982.
a. Identify the initial amount, the decay factor, and the annual percent decrease.
b. Use the graph to estimate when the number of records sold was 1 million.
4. You buy a new car for $30,000. The value of the car decreases by 15.7% each year.
a. Write an exponential decay model for the value of the car. Use the model to estimate the value after
3 years.
b. Estimate when the car will have a value of $800.
8.1 – 8.3 Word Problems: Pg. 2 of 5
Section 8.3 – Compound Interest
Interest paid on the initial investment, called the principal, and on previously earned interest.
(Interest paid only on the principal is called simple interest.)
5. You deposit $1000 in a bank account. Find the balance after 5 years for each of the following situations.
a. The account pays 2.5% annual interest compounded monthly.
b. The account pays 1.75% annual interest compounded quarterly.
Continuously Compounded Interest
As the number of times that interest is compounded per year increases, ________ increases.
6. You deposit $1000 in a bank account. Find the balance after 5 years for each of the following situations.
a. The account pays 2.5% annual interest compounded continuously.
b. The account pays 1.75% annual interest compounded continuously.
8.1 – 8.3 Word Problems: Pg. 3 of 5
Additional Practice
7. In 1990 the cost of tuition at a state university was $4300. During the next 8 years, the tuition rose 4% each
year.
a. Write a model that gives the tuition y(in dollars) t years after 1990.
b. What was the approximate cost of tuition in the year 2000?
8. Write an exponential decay model that describes the situation.
a. You buy a stereo system for $1780. Each year t, the value V of the stereo system decreases by 7%.
b. You drink a beverage with 230 milligrams of caffeine. Each hour h, the amount c of caffeine in your
system decreases by about 11%.
c. An adult takes 600 milligrams of ibuprofen. Each hour h, the amount i of ibuprofen in the person’s
system decreases by about 25%.
9. You deposit $500 in a bank account. Find the balance after 2 years for each of the following situations
a. The account pays 4% annual interest compounded yearly.
b. The account pays 3.5% annual interest compounded daily.
c. The account pays 1% annual interest compounded continuously.
10. You want to have $2500 after 2 years. Find the amount you should deposit for each of the situations described
below.
a. The account pays 2.25% annual interest compounded monthly.
8.1 – 8.3 Word Problems: Pg. 4 of 5
b. The account pays 2% annual interest compounded quarterly.
c. The account pays 5% annual interest compounded yearly.
d. The account pays 2.25% annual interest compounded continuously.
8.1 – 8.3 Word Problems: Pg. 5 of 5