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Warm Up

Graph Exponential Decay Functions. Warm Up. Lesson Presentation. Lesson Quiz. –3. 1. ANSWER. 27. 1. 2. 3. 5. 0. 2. –. –1. ANSWER. Warm-Up. Evaluate the expression without using a calculator. –2. 2. 3. 1.0025. ANSWER. Warm-Up.

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Warm Up

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  1. Graph Exponential Decay Functions Warm Up Lesson Presentation Lesson Quiz

  2. –3 1. ANSWER 27 1 2 3 5 0 2. – –1 ANSWER Warm-Up Evaluate the expression without using a calculator.

  3. –2 2 3 1.0025 ANSWER Warm-Up Evaluate the expression without using a calculator. 3. 4 + 1 ANSWER 10 4.A savings account pays 3% interest compounded monthly. What is the growth factor for this account?

  4. 1 2 Example 1 x Graph y = . SOLUTION STEP 1 Make a table of values. STEP 2 Plot the points from the table. STEP 3 Draw, from right to left, a smooth curve that begins just above the x-axis, passes through the plotted points, and moves up to the left.

  5. x a. Plot (0, 2) and .Then, from right to left, draw a curve that begins just above the x-axis, passes through the two points, and moves up to the left. 1 1 4 2 1, Example 2 Graph the function. a. Graphy = 2 . SOLUTION

  6. 1,– x 2 6 b. 5 5 Plot (0, –3) and . Then,from right to left, draw a curve that begins just below the x-axis, passes through the two points,and moves down to the left. Example 2 Graph the function. b. Graphy = –3 . SOLUTION

  7. x x 2. y = –2 2 3 3 4 1. y = Guided Practice Graph the function.

  8. 1 5 x 3. f(x) = 4 Guided Practice Graph the function.

  9. Graph y = 3 –2. State the domain and range. Begin by sketching the graph of y = , which passes through (0, 3) and . Then translate the graph left 1 unit and down 2 units. Notice that the translated graph passes through (–1, 1) and . 1 1 3 – 1 2 2 2 2 x 3 0, x+1 1, Example 3 SOLUTION The graph’s asymptote is the line y = –2. The domain is all real numbers, and the range isy > –2.

  10. Snowmobiles A new snowmobile costs $4200. The value of the snowmobile decreases by 10% each year. Example 4 • Write an exponential decay model giving the snowmobile’s value y (in dollars) after t years. Estimate the value after 3 years. • Graph the model. • Use the graph to estimate when the value of the snowmobile will be $2500.

  11. t y = a(1 –r) t = 4200(1 –0.10) t = 4200(0.90) When t = 3, the snowmobile’s value is y = 4200(0.90)3 = $3061.80. Example 4 SOLUTION STEP 1 The initial amount is a= 4200 and the percent decrease is r = 0.10. So, the exponential decay model is: Write exponential decay model. Substitute 4200 for aand 0.10 for r. Simplify.

  12. Example 4 STEP 2 The graph passes through the points (0, 4200) and (1, 3780).It has the t-axis as an asymptote. Plot a few other points. Then draw a smooth curve through the points. STEP 3 Using the graph, you can estimate that the value of the snowmobile will be $2500 after about 5 years.

  13. x–1 4.y = +1 x+1 1 2 5. y = 5 –2 4 3 Guided Practice Graph the function. State the domain and range.

  14. 3 4 x – 5 6. g(x) = –3 +4 Guided Practice Graph the function. State the domain and range.

  15. SOLUTION y = 4200(0.8)tAfter about 2 yr. Guided Practice 7.WHAT IF?In Example 4, suppose the value of the snowmobile decreases by 20% each year. Write and graph an equation to model this situation. Use the graph to estimate when the value of the snowmobile will be $2500.

  16. SOLUTION $3729.69 Guided Practice 8. SNOWMOBILE The value of a snowmobile has been decreasing by 7% each year since it was new. After 3 years, the value is $3000. Find the original cost of the snowmobile.

  17. x 1. Graphy = 4 .State the domain and range. ANSWER 1 2 domain: all real numbersrange:y > 0 Lesson Quiz

  18. x+2 2. Graphy = 3 +2 .State the domain and range. ANSWER 1 4 domain: all real numbersrange:y > 2 Lesson Quiz

  19. about $ 913 ANSWER after about 4 yr ANSWER Lesson Quiz 3. A new laptop computer costs $1500. The value of the computer decreases by 22% each year. a. Estimate the value of the computer after 2 years. b.Estimate when the computer will be worth $550.

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