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Learn how to recognize, set up, and solve problems involving exponential growth and decay. We explore key terminology associated with growth—such as "grow," "increase," and "depreciation,"—and understand how to calculate future values based on growth or decay rates over time. Through practical examples, like the appreciation of a home or the depreciation of technology, we showcase the necessary formulas and key components: final amount (A), original amount (C), rate (r), and time (t). Enhance your problem-solving skills in exponential functions!
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Day 2 Graph 1. 2. 3.
8.8 Exponential Growth & Decay • I can recognize, set up, and solve exponential growth and decay problems.
Exponential Growth Growth: Look for words like “grow,” “increase,” etc… A = final amount C = original amount r = rate of growth t = time in years
Exponential Decay Decay: Look for words like “depreciation,” “loses,” “decline,” etc… A = final amount C = original amount r = rate of growth t = time in years
Exponential GrowthExponential Decay Ex. 1A home bought in Frankfort increases in value at 8.5% per year. If the home is worth $125,000 today, how much will the house be worth in 5 years? A = C = r = t = ??? 125,000 .085 5
Exponential GrowthExponential Decay Ex. 2Michael Jordan’s autographed basketball cost $20,000.00 on E-Bay. If the basketball increases value at 4% per year, how much will it be worth in 8 years? A = C = r = t = ??? 20,000 .04 8
Exponential GrowthExponential Decay Ex. 3An iPod has a depreciation rate of 2% per year. If the original price was $400.00, what is the value of the iPod 2 years later? A = C = r = t = ??? 400 .02 2
Exponential GrowthExponential Decay Ex. 4A boat is purchased for $75,000. If it depreciates at a rate of 8% per year, how much will it be worth after 7 years? A = C = r = t = ??? 75000 .08 7
