Exponential Growth and Decay Unit 9 Day 3 Exponential Growth and Decay

Any quantity that grows or decays by a fixed percent at regular intervals is said to possess exponential growth or exponential decay. Many real world phenomena can be modeled by exponential growth or decay. studies of populations radioactive substances bacteria credit payments electricity temperatures

Exponential Growth vs. Decay Exponential Decay y = a∙bx y = a∙bx 0 < b < 1 b > 1

Growth or Decay? y = 5 ·2 x y = 4 ·0.87 x y = 10 ·0.02 x y = 6 ·1.5 x

Exponential Growth & Decay Models Growth: a(1 + r)x Decay: a(1 – r)x a = initial amount before measuring growth/decay r = growth/decay rate (often a percent) x = number of time intervals that have passed (1 + r) is called the growth factor (1 – r) is called the decay factor

Finding the Decay Factor The population decreased by 13% per year. Steps for calculating the decay factor: Step 1: Identify the percent of decrease. Step 2: Subtract the percent from 100% Step 3: Change to a decimal. To find the growth factor, the only difference is to add the percent to 100%

Example #1 The value of an iPad decreases at 35% per year. If the starting price of the iPad is $500, write the exponential function. How much will your iPad be worth after 5 years?

Example #2 Suppose the acreage of forest is decreasing by 2% per year because of development. If there are currently 4,500,000 acres of forest, determine the amount of forest land after 5 years.

Example #3 A bank account balance, b, for an account starting with s dollars, earning an annual interest rate, r, and left untouched for n years can be calculated as b = s(1 + r)n 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 Problems 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.

4) The pesticide DDT was widely used in the United States until its ban in 1972. DDT is toxic to a wide range of animals and aquatic life, and is suspected to cause cancer in humans. Write an equation to examine the 15 year half-life of 100 grams of DDT. How much DDT would be remaining after 45 years?

When you have read over the notes & completed the examples, check your answers with Ms. Taormina and take a CW Sheet on Exponential Growth & Decay. When you complete that, work on your Exam Review Packet.