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1. Exponents Review

1. Exponents Review. Remember, the following basic exponent rules:. 2. Exponential Functions Non-Linear. Exponential Functions are functions where the variable is the exponent. Switched from quadratic Examples: f(x) = 3 x P(r) = 2000(1.05) r f(x) = 4( ½ ) x. 3.

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1. Exponents Review

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  1. 1. Exponents Review • Remember, the following basic exponent rules:

  2. 2. Exponential Functions Non-Linear • Exponential Functions are functions where the variable is the exponent. • Switched from quadratic • Examples: f(x) = 3x • P(r) = 2000(1.05)r • f(x) = 4( ½ )x

  3. 3. Graphing Exponential Functions • Ex1 (I DO): f(x) = 3x • Plot at least 5 points to get a good sense of the function. • You may want to space your x values out to see growth • 3 decimal places Find these two first When x=0, y coord. is y-intercept

  4. 3. Graphing Exponential Functions • Ex1 (I DO): f(x) = 3x

  5. 3. Graphing Exponential Functions • Called exponential function because it grows exponentially • Output values start really small and get really big, really fast.

  6. 3. Graphing Exponential Functions • Ex2 (WE DO): f(x) = 2x • Plot at least 5 points to get a good sense of the function. • You may want to space your x values out to see growth • 3 decimal places Find these two first When x=0, y coord. is y-intercept

  7. 3. Graphing Exponential Functions • Ex1 (WE DO): f(x) = 2x

  8. 3. Graphing Exponential Functions • Ex2 (WE DO): f(x) = 4(1/2)x Find these two first When x=0, y coord. is y-intercept

  9. 3. Graphing Exponential Functions • Ex2 (WE DO): f(x) = 4(1/2)x

  10. Linear Exponential 4. Linear vs. Exponential Growth f(x) = 2x f(x) = 2x +2 times 2 +2 times 2 +2 times 2 +2 times 2 Constant Rate Add/Subtract the same value to increase output Constant Growth Rate Multiply by the same value to increase output (sometimes written as % change)

  11. 4. Linear vs. Exponential Growth Which rate of change is it: linear or exponential? Linear Exponential • Always stated in units (NOT percent) • Increase/Decrease is because of adding or subtracting (NOT multiplying) • Always stated in percent or multiplication factor (NOT units) • Increase/Decrease is because of multiplying (NOT adding) • a) The fish in the sea are decreasing by 10% every year • b) Mr. Vasu’s bank account increases by $3,000 every month Exponential: 10% change Linear: $3,000 change

  12. Constant Growth Rate y2 y1 = To find the constant mult. factor 5. How to find the Constant Multiplication Factor f(x) = 3x 0.333 0.111 3 = 1 0.333 3 = 9 3 3 = Must be consecutive ordered pairs 243 9 27 = 3.00 = 300%

  13. Constant Growth Rate y2 y1 = To find the constant mult. factor 5. How to find the Constant Multiplication Factor f(x) = 4(1/2)x 8 16 0.5 = 4 8 0.5 = 2 4 0.5 = 0.50 = 50%

  14. How to find the y-intercept? 6. How to find the Y-Intercept Remember: X=0 at the y-intercept f(x) = 3x f(x) = 4(1/2)x (0,1) is the y-intercept (0,4) is the y-intercept

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