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ET 3.1a

ET 3.1a. Investigate what happens to the graph when you use different values for a such that a>0 . Summarize your findings. What point do all of the graphs have in common? Why?. (0, 1) because a 0 =1. If a > 1, When a increases the function gets closer to the x & y-axis. .

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ET 3.1a

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  1. ET 3.1a Investigate what happens to the graph when you use different values for a such that a>0 . Summarize your findings. What point do all of the graphs have in common? Why? (0, 1) because a0=1 If a > 1, When a increases the function gets closer to the x & y-axis. If 0<a < 1, When a increases the function gets further from the x & y-axis.

  2. Definition of exponential function The exponential function f with base a is denoted by Where a > 0, a 1, and x is any real number Variable exponent Case 1: a > 1 Case 2: 0 < a < 1

  3. In the same coordinate plane, sketch the graph of What is the only difference between these graphs and those in the ET? x  - x means reflect y-axis

  4. Describe the transformation of the graphs of the exponential functions. State the Domain, Range, H.A., intercept Yes – Math Man still applies! Left 1 Right 1 Down 1 Up 1

  5. Describe the transformation of the graphs of the exponential functions. Reflect x-axis Reflect y-axis Left 4 Left 1 Up 4 Down 2 Reflect x-axis Reflect y-axis

  6. 3.1 Assignment • Day 1: 7-10, 17-22, 27, 31, 80

  7. ET 3.1b: Copy only the true equations.

  8. If , then n = m .Solve Strategy: Force the base numbers to be equal.

  9. Solve Your Turn! 1st ten

  10. Solve

  11. Solve

  12. True or False FALSE FALSE TRUE

  13. 3.1 Assignment • Day 1: 7-10, 17-22, 27, 31, 80 • Day 2: 45-52, 69, 73-76 • Day3: 53-63 Review of creating a scatter plot.

  14. ET 3.1c Graph State the domain, range, H.A. of f(x). Evaluate: Left 1 = 2.718281828… Down 3

  15. Formulas for Compound Interest t = years A = Account Balance (Your Money + Interest) P = principal (Your Money) r = interest rate (decimal) n compounds per year Continuous compounding

  16. Don’t copy this slide or the next. I=Prt • Invest $10,000 for one year earning 5% interest • Compounded yearly • Compounded semiannually • 1st 6 months • 2nd 6 months A = $10,500 A = $10,250 A = $10,506.25

  17. A = $10,125 • Invest $10,000 for one year earning 5% interest • Compounded quarterly • 1st quarter • 2nd quarter • 3rd quarter • 4th quarter A = $10,251.5625 A = $10,379.707 A = $10,509.45

  18. Compounded Annually Semiannually Quarterly Monthly Daily Hourly A = $10,500 A = $10,506.25 A = $10,509.45 Your turn A = $10,511.62 A = $10,512.67 A = $10,512.71

  19. Compounded Continuously A = $10,512.71 $ .00 A = $10,512.71 Hourly $ .04 Daily A = $10,512.67 $ 1.05 A = $10,511.62 Monthly $ 2.17 A = $10,509.45 Quarterly $ 3.20 Semiannually A = $10,506.25 $ 6.25 Yearly A = $10,500

  20. Brothers: Brennan & Dale each inherit $10,000. Brennan: 22 years old Buys a used Honda Civic and pays $200 to have the junk yard take it off his hands 6 years later. 10 years before he retires he saves $100,000 and invests the money in the same mutual funds as Dale. Dale: 22 years old Puts his money in a mutual fund and leaves it until he retires. On average it earns 12%.

  21. Brennan: “ I skate therefore I am skating.” I don’t need to worry about retirement. That is for old people. Besides I’ve put away 10 times as much as my brother Dale. 10 times. Hear me roar….of my own money.” Dale: “Doing what I love is what is important. It doesn’t matter that others don’t like to hear me sing. When they throw food I just think – yes I’m bringing home the bacon. Just do it! That is what I say. Besides I’m going to be a millionaire. My granddad gave me $10,000 & I’m going to retire in style.

  22. Money isn’t everything. I’m going to bless you with my voice for another 3 years. Age 62 Age 62 A =$332,011.69 A = $1,215,104.18 By the way… This is how much money Dale had when he was 51 & Brennan hadn’t even started saving. A = $1,741,644.56

  23. Dale had two grandchildren. When they were born he secretly placed $5,000 into some mutual funds averaging 12%. He wanted them to be able to follow their dreams and not have any worries about retirement. Both grandchildren retired multimillionaires at age 50. Age 62 A = $1,215,104.18 A = $2,017,143.967 Age 62 A = $1,741,644.56

  24. 3.1 Assignment • Day 1: 7-10, 17-22, 27, 31, 80 • Day 2: 45-52, 69, 73-76 • Day3: 53-63 Review of creating a scatter plot.

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