A genie offers you a choice: He will give you $50,000 right now OR He will give you 1 penny today, 2 tomorrow, 4 the next day and so on for a month. Which.

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Presentation transcript:

A genie offers you a choice: He will give you $50,000 right now OR He will give you 1 penny today, 2 tomorrow, 4 the next day and so on for a month. Which do you choose?

Exponential Growth and Decay Students will be able to:

Exponential Functions

Graphing Exponential Functions xy

Exponential Growth Initial value Rate of increase Time

Examples

 Take a piece of paper and fold it in half. Now do it again. And again. How many times can you fold it?  Imagine you could fold it as many times as you wanted. How high would the paper reach after 42 folds?  We can write an exponential equation for this! Each time you fold the paper, the height doubles. What so what is the growth factor?  A piece of paper is.004 inches thick, so this is our initial value. Folding Paper

Modeling Population Growth In 2000, the annual rate of increase in the US population was 1.24%. a.Find the growth factor for the population b.Write a function to model the population growth. c.Predict the population in 2015.

 You invest $5000 in an account that earns 2% monthly interest. How much will you have in your account after 3 years? Compounding Interest

Exponential Decay Initial value Rate of increase Time

 You want to buy a used Honda Civic that cost $20,000 when it was new in If it depreciates at 15% each year, how much will it cost for you to buy it now?  What is the decay factor?  What value do we know?  What do we want to find? Depreciation (the decline in the value of an item over time)

 For each of the following:  A) Does the equation represents growth or decay?  B) What is the growth/decay rate as a percentage? Growth or Decay?