1. 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.

2. 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.

3. 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.

4. Basic Exponential Graphs
Growth Decay

5. 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.

6. 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.

7. 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.

8. 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.

9. 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.

10. 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.

11. Homework 8.1 pg 469 Homework 8.2 pg #477
# 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.