1. Given the equation y = 650(1.075) x a)Does this equation represent growth or decay ?_______ b) What is the growth factor ? _____________ c) What is the rate of growth or decay ? ______________ d) What is the initial value ? _______________ e) Evaluate for x = 9 _______________

Describe the transformations Is this a growth or decay model?

Topics for Unit 3B Characteristics of Functions Characteristics of Functions Properties – domain and range, increasing and decreasing, intercepts, asymptotes Properties – domain and range, increasing and decreasing, intercepts, asymptotes Rate of Change Rate of Change Transformations Transformations Sequences vs. Functions Sequences vs. Functions Word Problems Word Problems Growth and Decay Models Growth and Decay Models

1. Find the domain and range of the graph.

2. What is the asymptote? What is the x-intercept? y-intercept?

3. Identify the following: Domain: Range: x-int: y-int: Increasing or Decreasing

4. Describe the transformations. f(x) = 3(2) x + 1

5. Write an equation of an exponential with a base of 5 given the following transformations: f(x)= - (5) x – 4 - 3

6. The yearbook staff is unpacking a box of school yearbooks. The sequence 281, 270, 259, 248… represents the total number of ounces that the box weighs as each yearbook is taken out. Write a sequence for the situation. After 20 yearbooks were unpacked, how much did the box weigh? a n = -11n ounces

7. Amelia is SCUBA diving in Grand Cayman. She is currently 135 feet under water but she is swimming towards the surface at a rate of 15 feet per minute. Write an equation that represents the situation. What is the slope of your equation and what does it represent in this scenario? How long will it take Amelia to reach the surface? Be able to explain your answer. y= 15x – ; how much Amelia is increasing by 9 mins; At 9 mins Amelia has reached 0

8. Consider the following for your summer job: Option 1: You can be paid $20 an hour. Option 2: You can get $1 the first hour and your hourly rate would double every hour. Write the equation/sequence for each option. If you only worked 10 hours which job would you want? f(x)= 20n a n = 1(2) n-1 Option 1 would pay $200, and Option 2 would pay $512

9. The tuition at a private college is $15,000 and has about a 7.2% annual increase. a) Write an exponential equation describing this situation. b) How much will the tuition be 5 years from now? y = 15,000(1.072) x $21,235.63

10. You purchase a stereo system for $830. The value of the stereo system decreases 13% each year. a)Write an exponential equation describing the situation. b) What is the value of the system in 3 years? y = 830(.87) x $546.56

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