Exponential Growth vs Decay Exponential Growth y abx
Exponential Growth vs. Decay Exponential Growth y = a∙bx b>1 Exponential Decay y = a∙bx 0<b<1
Exponential Growth and Decay Models y = a(1 + a = starting amount x r) r = rate r is positive for growth r is negative for decay
Growth or decay? What percentage? 1. y = 67(1. 06)x 2. y = -98(. 87)x 3. y = 300(1. 27)x 4. y = 142(. 35)x 5. y = 5(2)x
Example 1: i. Pads y = a(1 + r)x The value of an i. Pad decreases at 35% per year. If the starting price of the i. Pad is $500, write the exponential function. How much will the i. Pad be worth after 5 years?
Example 2: Forest y = a(1 + r)x Suppose the acreage of forest is decreasing by 2% per year because of development. If there are currently 4, 500, 000 acres of forest, how much forest land will there be in 6 years?
Example 3: Investing y = a(1 + r)x Find a bank account balance to the nearest dollar, if the account starts with $100, has an annual rate of 4%, and the money is left in the account for 12 years.
Half Life • Some unstable substances, like plutonium, decay over time. To measure the rate of decay, scientists refer to their “half life. ” • The half life is the time it takes for half the initial amount of the substance to decay.
Example 4: DDT y = a(1 + r)x The pesticide DDT was widely used in the United States until its ban in 1972. Write an equation that models the 15 year half-life of 100 grams of DDT. How much DDT would be remaining after 45 years?
Example 5: 228 Ac y = a(1 + r)x 228 Ac has a half life of 6. 13 hours. Write an equation that models the half life of a 5 mg sample. How much 228 Ac would be remaining after one day?
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