advertisement

Notes – Lesson 8.1 Algebra 2 Name __________________________ Examples for questions 1-8. Graph each function. Set up tables on calculator. 1. y = 3(10)x 2. y = 9(3)X Examples for questions 9 and 39. 1. Exponential Function: _____________________ where _________________________________________ 2. a is the _________________________________ b is called the __________________________________________ 3. You can use an exponential function to model population growth. If you know the rate of increase r, you can find the growth factor by using the equation or rate of decrease ______________________________ _________________ Example: A new car sells for $18,000 depreciates 25% each year. Write a function that models the value of the car. Find the value of the car after 4 yr. The bear population increases at a rate of 2% per year. There are 1573 bear this year. Write a function that models the bear population. How many bears will there be in 10 yr? The population of an endangered bird is decreasing at a rate of 0.75% per year. There are currently about 200,000 of these birds. Write a function that models the bird population. How may birds will there be in 100yr? Examples for questions 10-15. Writing an Exponential Function 1. Write an exponential function y = ab x for a graph that includes (2, 2) and (3, 4). y = abx y = abx Use your equation for a Substitute (2, 2) Substitute (3, 4) Solve for a. Plug in a. Plug in b. Simplify Simplify Solve for b. 2. (4, 8), (6, 32) 3. (2, 18), (5, 60.75) Examples for questions 16-23. Graph y = 14(.95)x growth or decay? ________________ Rule: if b > 1 ________________________________, y = 5(1.05)x growth or decay? ________________ if 0 < b < 1 ______________________________ Growth or Decay? y = 100(0.12)x __________________-- y = 0.5(5)x __________________ Examples for questions 36-41. For each function, find the annual percent increase or decrease that the function models. 2. y = 30.69( 85 ) x 1. y = 1700(0.75)x 3. y = 984.5(1.73)x Examples for questions 46 – 53. 1. +45% 2. -10% 3. -40% 4. -200% Examples for questions 35. Suppose you want to buy a used car that costs $11,800. the expected depreciation of the car is 20% per year. Estimate the depreciated value of the car after 6 years. Assignment Page 434: 1-31(odd), 35, 36-41(all), 46-53(all)