8.1 Exponential Growth 𝑇ℎ𝑒 𝑏𝑎𝑠𝑖𝑐 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑜𝑓𝑎 𝑔𝑟𝑜𝑤𝑡ℎ 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑦=𝑎∙ 𝑏 𝑥 where a is the starting point larger than 0. b is the ratio multiplier larger than 1. b doubled is the number 2, tripled is 3 or adding a decimal . X is usually a time seconds , hours, years.

8.2 Exponential Decay 𝑇ℎ𝑒 𝑏𝑎𝑠𝑖𝑐 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑜𝑓𝑎 𝐷𝑒𝑐𝑎𝑦 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑦=𝑎∙ 𝑏 𝑥 where a is the starting point larger than 0. b is in between 0 and 1. b is a percent of the original starting amount. X is usually a time seconds , hours, years.

Concept #1 Parts of the exponent graph. The y intercept is when x is zero. The starting asymptote is only horizontal and the line y=0. This will change . Let us analyze the graphs.

Basic Exponential Graphs Growth Decay

Example #1 Properties The function 𝑦=12 2 𝑥 Growth or Decay Starting amount and the y-intercept.______ Asymptote ___________ The new asymptote is always the shift vertically.

Example #1 Properties The function 𝑦=12 2 𝑥 Growth or Decay Starting amount and the y-intercept.______ Asymptote ___________ The new asymptote is always the shift vertically.

Example #2 Properties The function 𝑦=34 1.5 𝑥 +50 Growth or Decay Starting amount and the y-intercept.______ Asymptote ___________ The new asymptote is always the shift vertically.

Example #2 Properties The function 𝑦=34 1.5 𝑥 +50 Growth or Decay Starting amount and the y-intercept.______ Asymptote ___________ The new asymptote is always the shift vertically.

Example #3 Properties The function 𝑦=20 .80 𝑥 −11 Growth or Decay Starting amount and the y-intercept.______ Asymptote ___________ The new asymptote is always the shift vertically.

Example #3 Properties The function 𝑦=20 .80 𝑥 −11 Growth or Decay Starting amount and the y-intercept.______ Asymptote ___________ The new asymptote is always the shift vertically.

Homework 8.1 pg 469 Homework 8.2 pg #477 #13-18 asymptote , y int and Graph Homework 8.2 pg #477 #11-18 all, #25,26,29,30,33 Find the starting point and the Decay ratio. Graph each.