5 3 Exponential Functions 5 3 Exponential Functions

5. 3 – Exponential Functions

5. 3 Exponential Functions Objectives: � Understand the exponential growth/decay function family. � Graph exponential growth/decay functions. � Use exponential functions to model in real life. Vocabulary: exponential function, rule of 72, exponential growth, exponential decay

5. 3 Exponential Functions base b increasing decreasing

Yesterday: When the rate is given, the following formulas are most useful: Growth: Decay: y = a (1 + r ) t y = a (1 – r ) t When the rate is not given, the following formula is most useful: y = a∙b t/k ****where k = the time needed to multiply a by b

Example 1: A bank advertises that if you open a savings account, you can double your money in 12 years. Write an equation to express the amount of money after t years.

Example 2: The half-life of a radioactive isotope is 5 days. a) If 3. 2 kg is present now, what is the equation that models this situation after t days? b) At what rate does the substance decay each day?

Rule of 72: �A method for estimating how long an investment will take to double. Doubling time = 72/r *where r is left as a percentage

Example 3: How long does it take to double an investment that grows at the rate of: a) 9% per year? a) 6% per month?

Example 4: You have a new computer for $2100. In 5 years, the computer is worth $500. What is the depreciation rate for the computer?

Homework: � Finish the worksheet