8.2 exponential decay
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The document discusses exponential decay functions which have the form f(x) = abx, where 0 < b < 1. It provides examples of graphing exponential decay functions and explains that they approach the x-axis from the right side. Exponential decay models can model quantities that decrease by a fixed percentage each year, such as the value of a car over time or record sales from year to year.
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8.2 exponential decay
- 2. Exponential Decay Functions Much like exponential growth functions, they have the form f(x) = abx, but instead have 0 < b < 1. Decide whether each is an exponential growth or exponential decay function:
- 3. What’s the Shape? Let’s make a table to find the general shape. If we use as an example: x -3 -2 -1 0 1 2 3
- 4. To graph (when 0 < b < 1): Same as for b > 1, but curve is drawn from right to left. Graph now approaches the x-axis on the right side (instead of the left side). Example: Graph
- 7. General Exponential Functions General form: Same as before: Sketch parent graph Shift using h and k Example: Graph Domain: Range:
- 8. Your Turn! Graph the function and state the domain and range.
- 9. Exponential Decay Models For quantities that decrease by a fixed percent each year, the amount after t years is: where a is the initial amount and r is the percent decrease. (1 – r) is the decay factor
- 10. Example You buy a new car for $24,000. The value of the car decreases by 6% each year. Write an exponential decay model that describes the situation. What will be the value of the car after 2 years?
- 11. Your Turn! From 1982 to 1993, the number of records sold in the US decreased by 61% per year. There were 265 million records sold in 1982. Write an exponential decay model. How many records were sold in 1991?