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:
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
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
General Exponential Functions General form: Same as before: Sketch parent graph Shift using h and k Example: Graph Domain: Range:
Your Turn! Graph the function and state the domain and range.
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
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?
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?