8.1 Exponential Growth 𝑇ℎ𝑒 𝑏𝑎𝑠𝑖𝑐 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑜𝑓𝑎 𝑔𝑟𝑜𝑤𝑡ℎ 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑦=𝑎∙ 𝑏 𝑥 where a is the starting amount. b is the ratio multiplier larger than 1. 𝑦=𝑎∙ 𝑏 𝑥−ℎ +𝑘

8.2 Exponential Decay 𝑇ℎ𝑒 𝑏𝑎𝑠𝑖𝑐 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑜𝑓𝑎 𝐷𝑒𝑐𝑎𝑦 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑦=𝑎∙ 𝑏 𝑥 where a is the starting amount. b is in between 0 and 1. 𝑦=𝑎∙ 𝑏 𝑥−ℎ +𝑘

Basic Exponential Graphs Growth Decay

Finding the graph and Properties Find the Shift of the graph. h,k up down. And use a chart to sketch a graph. Y-intercept is when x=0 Domain ,Range, Asymptote

Example #1 The function 𝑦=12 2 𝑥 Growth or Decay Starting amount y-intercept Shift horizontally Shift vertically Asymptote Domain Range Graph X Y

Example #2 The function 𝑦=2 3 (𝑥+5) −7 Growth or Decay Starting amount y-intercept Shift horizontally Shift vertically Asymptote Domain Range Graph X Y

Example #3 The function 𝑦= 24 1 2 𝑥 Growth or Decay Starting amount y-intercept Shift horizontally Shift vertically Asymptote Domain Range Graph X Y

Example #4 The function 𝑦= 50 1 2 (𝑥+7) +2 Growth or Decay Starting amount y-intercept Shift horizontally Shift vertically Asymptote Domain Range Graph X Y

Concept #1 Steps to find equations. Will be done at a later date……love Bonin!!!!! The y intercept is used to find a. Use the y-int and plug into the equation. 𝑦=𝑎∙ 𝑏 𝑥−ℎ +𝑘 Find a.

Homework 8.1 pg 469 Homework 8.2 pg #477 #13-24 all, 25-41 odd