Objectives:  Understand the exponential growth/decay function family.  Graph exponential growth/decay functions.  Use exponential functions to model.

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Presentation transcript:

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

base b increasing decreasing

When the rate is given, the following formulas are most useful: Growth:y = a (1 + r ) t Decay: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 Yesterday:

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 1:

The half-life of a radioactive isotope is 5 days. a) If 3.2kg is present now, what is the equation that models this situation after t days? b) At what rate does the substance decay each day? Example 2:

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

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

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

 Finish the worksheet