Algebra 3 Lesson 5.2 A Objective: SSBAT model exponential growth and decay. Standards: C; S

Modeling Exponential Growth and Decay y = ab x a = original amount in problem b = Growth or Decay factor

Finding the value of b Exponential Growth b = 1 + % * change % to a decimal 1 st * Exponential Decay b = 1 – % * Change % to decimal 1 st *

1. A car is purchased for $18,000. Its value depreciates 25% each year. a)Write an exponential function to model the value of the car, y, after x years.  This is a Decay problem a = y = 18000(.75) x b = 1 – 0.25 b =.75

1. Continued. b) Find the value of the car after 9 years. Let x = 9 and solve equation for y y = 18000(.75) 9 y = After 9 years the car is worth $1,351.52

2.The bear population increases at a rate of 2% per year. There are 1573 bears this year. a) Write an exponential equation to represent the number of bears, y, after x years.  This is exponential growth a = 1573 b = b = 1.02 y = 1573(1.02) x

2.continued How many bears will there be in 13 years?  let x = 13 y = 1573(1.02) 13 y = There will be 2034 bears.

3.The population of an endangered bird is decreasing at a rate of 0.75% per year. There are currently 200,000 of these birds. a) Write an exponential function that models the bird population, y, after x number of years. b) How many birds will there be in 100 years? a = 200,000 b = = y = (0.9925) x y = (0.9925) 100 y = 94, There will be 94,206 birds

4.The population of Mexico City was 18,131,000 in the year The projected average growth is 0.39%. a) Write an exponential function that models the population, y, after x number of years. b) Find the projected population for the year Let x = 0 represent the year a = 18,131,000 b = = y = (1.0039) x 2010  x = 10 y = (1.0039) 10 y = 18,850,648.71

Homework 5.2 A