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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.
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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 • In nature and in the real world, things that change over time are often best modeled with an exponential function. • An exponential function is when the independent variable (the x) is the exponent. • The general form of this equation is where and .
Graphing Exponential Functions To graph exponential functions, make a table and plot the points. Ex: Will the graph ever cross the x-axis?
Exponential Growth Time Initial value Rate of increase • An exponential function where • b is called the growth factor. • If you know the rate, r, at which something is increasing, you can find the growth factor, b. • Often times we re-write our function like this:
Examples • Find the growth factors and initial values in each of the following equations • Challenge: What is the rate of increase in #3?
Folding Paper 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.
Modeling Population Growth In 2000, the annual rate of increase in the US population was 1.24%. • Find the growth factor for the population • Write a function to model the population growth. • Predict the population in 2015.
Compounding Interest You invest $5000 in an account that earns 2% monthly interest. How much will you have in your account after 3 years?
Exponential Decay Time Rate of increase Initial value • An exponential function where • b is called the decay factor • If you know the rate of decrease, r, then
Depreciation(the decline in the value of an item over time) • You want to buy a used Honda Civic that cost $20,000 when it was new in 2006. 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?
Growth or Decay? • For each of the following: • A) Does the equation represents growth or decay? • B) What is the growth/decay rate as a percentage?