Essential Skills:Solve problems involving exponential growthSolve problems involving exponential decay

Equation for Exponential Growth y = a(1 + r)t

▪ y: the final amount▪ a: the initial amount▪ r: rate of change (as a decimal; r > 0)▪ t: time

y = a(1 + r)t

Example 1A In 2008, the town of Flat Creek had a

population of about 280,000 and a growth rate of 0.85% per year. Write an equation to represent the population of Flat Creek since 2008.▪ (initial amount) a = 280000▪ (rate) r = 0.85% = 0.0085▪ y = 280000(1 + 0.0085)t

▪ y = 280000(1.0085)t Simplify

Example 1B In 2008, the town of Flat Creek had a

population of about 280,000 and a growth rate of 0.85% per year. According to the equation, what will be the population in the year 2018?▪ y = 280000(1.0085)t

▪ In 2018, t = 2018 – 2008, so t = 10.▪ y = 280000(1.0085)10

▪ y ≈ 304,731

1 2 3 4

0% 0%

29%

71%1. y = 4500(1.0015)2. y = 4500(1.0015)t

3. y = 4500(0.0015)t

4. y = (1.0015)t

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1 2 3 4

0% 0%

88%

12%

1. About 9000 students2. About 4450 students3. About 4540 students4. About 4790 students

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Equation for Compound Interest A = P(1 + r/n)nt

▪ A: the current amount▪ P: the principal (initial) amount▪ r: annual interest rate (as a decimal)▪ n: number of times each year interest is

compounded▪ t: time in years

A = P(1 + r/n)nt

When Jing May was born, her grandparents invested $1000 in a fixed rate savings account at a rate of 7% compounded annually. The money will go to Jing May when she turns 18 to help with her college expenses. What amount of money will Jing May receive from the investment? P = 1000 r = 7% = 0.07 n = 1 (annually = once per year) t = 18 years▪ A = 1000(1 + 0.07/1)1 ● 18

▪ A = 1000(1.07)18

▪ A ≈ $3379.93

1 2 3 4

71%

6%

18%

6%

1. About $46822. About $52023. About $45024. About $4582

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Equation for Exponential Decay y = a(1 – r)t

▪ y: the final amount▪ a: the initial amount▪ r: rate of change (as a decimal; 0 < r < 1)▪ t: time

y = a(1 – r)t

Example 3A During an economic recession, a charitable

organization found that its donations dropped by 1.1% per year. Before the recession, its donations were $390,000. Write an equation to represent the charity’s donations since the beginning of the recession.▪ (initial amount) a = 390000▪ (rate) r = 1.1% = 0.011▪ y = 390000(1 – 0.011)t

▪ y = 390000(0.989)t Simplify

Example 3B During an economic recession, a

charitable organization found that its donations dropped by 1.1% per year. Before the recession, its donations were $390,000. Estimate the amount of donations 5 years after the start of the recession▪ y = 390000(0.989)t

▪ y = 390000(0.989)5

▪ y ≈ 369,016.74

1 2 3 4

0%

28%

39%

33%

y = (0.975)t

y = 24000(0.975)t

y = 24000(1.975)t

y = 24000(0.975)

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1 2 3 4

0% 0%

100%

0%

1. About $23,7352. About $21,2953. About $22,2454. About $24,975

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Assignment Page 434 – 435 Problems 1 – 11, odds