1. Essential Skills: Solve problems involving exponential growth Solve problems involving exponential decay

2.  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

3.  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

4.  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

5. 1. y = 4500(1.0015) 2. y = 4500(1.0015) t 3. y = 4500(0.0015) t 4. y = (1.0015) t

6. 1. About 9000 students 2. About 4450 students 3. About 4540 students 4. About 4790 students

7.  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

8.  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

9. 1. About $4682 2. About $5202 3. About $4502 4. About $4582

10.  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

11.  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

12.  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

13.  y = (0.975) t  y = 24000(0.975) t  y = 24000(1.975) t  y = 24000(0.975)

14. 1. About $23,735 2. About $21,295 3. About $22,245 4. About $24,975

15.  Assignment  Page 434 – 435  Problems 1 – 11, odds