A function of the form: y = ab x where a ≢ 0, b > 0, and b ≢ 1 It is a nonlinear function. Exponential Growth (8.5) y = ab x where a>0 and b>1 (rises.

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Presentation transcript:

A function of the form: y = ab x where a ≢ 0, b > 0, and b ≢ 1 It is a nonlinear function. Exponential Growth (8.5) y = ab x where a>0 and b>1 (rises from left to right) Exponential Decay (8.6) y = ab x where a>0, and 0<b<1 (falls from left to right)

1. Take 1 yard of yarn which would be 1 unit in length. Fold and cut in half where you have 2 pieces which are each ½ in length. 2. Fold, repeat, and fill out the table. Stage# of piecesLength –each piece

3. Write a function that models the # of pieces of yarn at stage x 4. Use the function to find the # of pieces at stage Write a function that models the length of each new piece of yarn at stage x 6. Use the function to find the length of each new piece of yarn at stage 10

Linear: y = 3x + 2 **Change in both x and y are addition (could be subtraction). Exponential: y = 2 * 3 x **Change in y is multiplication (could be division). Note: y = a * b x where a is “0” term and b is the change x-2012 y x-2012 y

7. Change: a = b = So... y = x-2012 y1/811/271/91/31

8. Change: a = b = So... y = x-2012 y

9. y = 4 x 10. y = (4/3) x X-2012 y X-2012 y

11. Graph y = (1/4). 2 x and y = (-1/4). 2 x. Compare with the graph of y = 2 x X-2012 y = 2 x y = (1/4). 2 x y = (-1/4). 2 x

12. One Computer Industry expert reported that there were about 600 million computers in use worldwide in 2001 and that the number was increasing at an annual rate of about 10% a. Write a function that models the number of computers in use over time. b. Use the function to predict the number of computers used worldwide in 2009.

y = a(1+r) t where a=initial investment, r=annual rate, t=# years invested 13. You put $500 in a savings account that earns 5% annual interest compounded yearly. You do not make any deposits or withdrawals. How much will your investment be worth in 4 years?

8.5 Practice B Worksheet