# Essential Skills: Solve problems involving exponential growth Solve problems involving exponential decay

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

• Equation for Exponential Growthy = a(1 + r)ty: the final amounta: the initial amountr: rate of change (as a decimal; r > 0)t: time

• y = a(1 + r)tExample 1AIn 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% = 0.0085y = 280000(1 + 0.0085)ty = 280000(1.0085)tSimplify

• Example 1BIn 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)tIn 2018, t = 2018 2008, so t = 10.y = 280000(1.0085)10y 304,731

• y = 4500(1.0015)y = 4500(1.0015)ty = 4500(0.0015)ty = (1.0015)t

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• Equation for Compound InterestA = P(1 + r/n)ntA: the current amountP: the principal (initial) amountr: annual interest rate (as a decimal)n: number of times each year interest is compoundedt: time in years

• A = P(1 + r/n)ntWhen 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 = 1000r = 7% = 0.07n = 1 (annually = once per year)t = 18 yearsA = 1000(1 + 0.07/1)1 18A = 1000(1.07)18A \$3379.93

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• Equation for Exponential Decayy = a(1 r)ty: the final amounta: the initial amountr: rate of change (as a decimal; 0 < r < 1)t: time

• y = a(1 r)tExample 3ADuring 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 charitys donations since the beginning of the recession.(initial amount) a = 390000(rate) r = 1.1% = 0.011y = 390000(1 0.011)ty = 390000(0.989)tSimplify

• Example 3BDuring 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 recessiony = 390000(0.989)t y = 390000(0.989)5y 369,016.74

• y = (0.975)ty = 24000(0.975)ty = 24000(1.975)ty = 24000(0.975)

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• AssignmentPage 434 435Problems 1 11, odds

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