Do Now: ~pick up the calendar and grab a calculator Take out a piece of paper and fold it in half. Count the number of rectangles you have and record on a table What do you notice about the data recorded on the table? What type of function do you think this table represents? # of folds 1 2 3 4 5 6 # of rectangles

Exponential Functions A function of the form y = a • bx # of folds 1 2 3 4 5 6 # of rectangles 8 16 32 64

Let’s find the function using the calculator # of folds 1 2 3 4 5 6 # of rectangles 8 16 32 64 In your calculator: STAT⇛Edit⇛L1⇛Enter the number of folds L2⇛Enter the number of rectangles STAT⇛Calc ⇛ExpReg(0) ⇛Enter ⇛Enter Out should come an exponential Function… What is the function after plugging in the variables? y=1•2x

What did you notice about the graph of the exponential function? Do you think it is the same for all exponential functions?

Let’s find out… Use your calculator to fill out the table: x 1 2 3 4 5 6

Graphing After you fill out the chart, graph each function using a different colored pencil Graph the first two functions on the first grid and the second two functions on the second grid

What are the differences between the two graphs? What are the similarities between the two graphs?

Do these graphs have the same similarities or differences?

What are the differences or similarities between the two graphs?

Exponential Functions Exponential Functions where b > 1 are increasing Increasing = Up Exponential Functions where b < 1 (fractions) are decreasing Decreasing = Do

Decreasing or increasing Fill out the chart: Decreasing or increasing y-intercept

Fill out the next table and graph 1 2 3 4 5 6

Looking at the tables/graph… Increasing/ decreasing y-intercept How does the c term affect the exponential function? How does the a term affect the exponential function?

Evaluating Exponential Fucntions

Evaluating… We will be able to use a calculator to solve the functions: Make sure you are careful about parentheses!!!!

Evaluate: f(x) = 6x for x = 2 f(x) = 4•2x for x = 3

Finance: An investment of $5000 doubles in value every decade. The function f(x) = 5000•2x where x is the number of decades, models the growth of the value of the investment. How much is the investment worth after 30 years? How much is the investment worth after 100 years?

Wildlife Management A population of 75 foxes in a wildlife preserve quadruples in size every 15 years. The function y = 75 • 4x where x is the number of 15 year periods, models the population growth. How many foxes will there be after 45 years? How many foxes will there be after 60 years?

Independent Practice Work on the worksheet independently.