1. Exponential Growth and Decay
ALGEBRA 1 LESSON 6-3
(For help, go to Lesson 4-3.)
Use the formula I = prt to find the interest for principal p, interest rate r, and time t in years.
1. principal: $1000; interest rate: 5%; time: 2 years
2. principal: $360; interest rate: 6%; time: 3 years
3. principal: $2500; interest rate: 4.5%; time: 2 years
4. principal: $1680; interest rate: 5.25%; time: 4 years
5. principal: $1350; interest rate: 4.8%; time: 5 years
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2. Exponential Growth and Decay
ALGEBRA 1 LESSON 6-3
Solutions
1. l = prt = ($1000)(0.05)(2) = $50(2) = $100
2. l = prt = ($360)(0.06)(3) = $21.60(3) = $64.80
3. l = prt = ($2500)(0.045)(2) = $112.50(2) = $225
4. l = prt = ($1680)(0.0525)(4) = $88.20(4) = $352.80
5. l = prt = ($1350)(0.048)(5) = $64.80(5) = $324
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3. Exponential Growth and Decay
ALGEBRA 1 LESSON 6-3
In 1998, a certain town had a population of about 13,000 people. Since 1998, the population has increased about 1.4% a year.
a. Write an equation to model the population increase.
Relate:  y = a • bx
Use an exponential function.
Define:
Let x = the number of years since 1998.
Let y = the population of the town at various times.
Let a = the initial population in 1998, 13,000 people.
Let b = the growth factor, which is
100% + 1.4% = 101.4% =
Write: y = 13,000 • 1.014x
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4. Exponential Growth and Decay
ALGEBRA 1 LESSON 6-3
(continued)
b. Use your equation to find the approximate population in 2006.
y = 13,000 • 1.014x
y = 13,000 •
2006 is 8 years after 1998, so substitute 8 for x.
Use a calculator. Round to the nearest
whole number.
14,529
The approximate population of the town in 2006 is 14,529 people.
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5. Exponential Growth and Decay
ALGEBRA 1 LESSON 6-3
Suppose you deposit $1000 in a college fund that pays 7.2% interest compounded annually. Find the account balance after 5 years.
Relate:  y = a • bx
Use an exponential function.
Define:
Let x = the number of interest periods.
Let y = the balance.
Let a = the initial deposit, $1000
Let b = 100% + 7.2% = 107.2% =
Write: y = 1000 • 1.072x
= 1000 •
Once a year for 5 years is 5 interest periods. Substitute 5 for x.
Use a calculator. Round to the nearest cent.
The balance after 5 years will be $
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6. Exponential Growth and Decay
ALGEBRA 1 LESSON 6-3
Suppose the account in the above problem paid interest compounded quarterly instead of annually. Find the account balance after 5 years.
Relate:  y = a • bx
Use an exponential function.
Define:
Let x = the number of interest periods.
Let y = the balance.
Let a = the initial deposit, $1000
Let b = 100% + There are 4 interest periods in
1 year, so divide the interest into 4 parts.
= = 1.018
7.2% 4
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7. Exponential Growth and Decay
ALGEBRA 1 LESSON 6-3
(continued)
Write: y = 1000 • 1.018x
= 1000 •
Four interest periods a year for 5 years is 20 interest periods. Substitute 20 for x.
Use a calculator.
Round to the nearest cent.
The balance after 5 years will be $
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8. Exponential Growth and Decay
ALGEBRA 1 LESSON 6-3
Technetium-99 has a half-life of 6 hours. Suppose a lab has 80 mg of technetium-99. How much technetium-99 is left after 24 hours?
In 24 hours there are four 6-hour half lives.
After one half-life, there are 40 mg.
After two half-lives, there are 20 mg.
After three half-lives, there are 10 mg.
After four half-lives, there are 5 mg.
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9. Exponential Growth and Decay
ALGEBRA 1 LESSON 6-3
Suppose the population of a certain endangered species has decreased 2.4% each year. Suppose there were 60 of these animals in a given area in 1999.
a. Write an equation to model the number of animals in this species that remain alive in that area.
Relate:  y = a • bx
Use an exponential function.
Define:
Let x = the number of years since 1999
Let y = the number of animals that remain
Let a = 60, the initial population in 1999
Let b = the decay factor, which is 100% % = 97.6% = 0.976
Write: y = 60 • 0.976x
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10. Exponential Growth and Decay
ALGEBRA 1 LESSON 6-3
(continued)
b. Use your equation to find the approximate number of animals remaining in 2005.
y = 60 • 0.976x
y = 60 •
2005 is 6 years after 1999, so substitute 6 for x. 52
Use a calculator. Round to the nearest whole number.
The approximate number of animals of this endangered species remaining in the area in 2005 is 52.
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11. Exponential Growth and Decay
ALGEBRA 1 LESSON 6-3
1. Identify the original amount a and the growth factor b in the exponential function y = 10 • 1.036x.
2. A population of 24,500 people has been increasing at a rate of 1.8% a year. What will be the population in 15 years if it continues at that rate?
3. Write an exponential function to represent $2000 principal earning 5.6% interest compounded annually.
4. Find the account balance on $3000 principal earning 6.4% interest compounded quarterly for 7 years.
5. The half-life of a certain substance is 4 days. If you have 100 mg of the substance, how much of it will remain after 12 days?
6. The value of a $1200 computer decreases 27% annually. What will be the value of the computer after 3 years?
a = 10, b = 1.036
about 32,017 people
y = 2000 • 1.056x
about $
12.5 mg
about $466.82
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