Exponential Decay
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Exponential decay formulas use an initial amount, a decay factor, and time to model how a quantity decreases over time. The document provides the formula y=a*b^x, where a is the initial amount, b is the decay factor less than 1, and x is time. It gives examples of using the formula to model radioactive decay from cancer treatment over time and decreasing milk consumption in the US each year since 1975, which has decreased by 4.5% annually.
Exponential Decay
- 2. Decay Formula y= a b x a > 0 & b = 1 - rate a is the starting amount b is the base (decay factor) Don’t forget to convert the rate from a % to a decimal x is the number of decreases
- 3. Decay Example 1 To treat some forms of cancer, doctors use radioactive iodine. Use the graph on page 373 to find out how much iodine is left in the patient 8 days after a patient receives a dose of 20mCi (millicuries). Since the x value represents the days, the y value represents the amount of iodine left -> 10. How much is left after 24 days? About 2.5
- 4. Decay Example 2 An exponential function models the amount of whole milk each person in the United States drinks in a year. Graph the function y=21.5 ● 0.955 x , where y is the number of gallons of whole milk and x is the number of years since 1975. What procedures will you use to graph this function?
- 5. Decay Example 3 Use the equation y=21.5 ● 0.955 x to find the annual percent of decrease in whole milk consumption in the United States. .955 = 95.5% 100% - 95.5% = 4.5% decrease per year