1. Good morning
Happy Friday

2. Exponentials Initial value Growth or decay factor
Re-call exponential form is 𝑦=𝑎∗ 𝑏 𝑥 , a≠0, and b>0
𝑎 represents:
Initial value
𝑏 represent the
Growth or decay factor

3. Is it growth or decay?
For each I.D. growth or decay, initial value and growth/decay factor: 1) 𝑦=8 3 𝑥 2) 𝑦=2 1 2 𝑥 3) 𝑦= 𝑥 4) 𝑦= 𝑥

4. Answers Growth, a= 8 and factor is b= 3
Decay, a = 2 and factor is b= ½
Growth a= 1/3 and factor is b=2
Decay a= and factor is b=0.25

5. Good Morning
Exponentials

6. Sketching a graph Make a table of values: 𝑦= 3 𝑥 x y -1 1 2 3 1/3 1 31 2 3
1/3 1 3 9 27

7. Plot values to get the graph

8. Finding equations
Given points: 0,1 𝑎𝑛𝑑 2, 36 Find the equations by substituting points in and solving for “a” and “b”

9. By Hand Use equation 𝑦=𝑎∗ 𝑏 𝑥 to solve for a. when x=0 then y=1.
So 1=𝑎∗ 𝑏 0 well 𝑏 0 =1 so
𝑎=1
Now use second point and solve for b.
36=1∗ 𝑏 2
So 𝑏=±6 but we know 𝑏>0 so
B=6

10. SO our equation is
𝑦=1∗ 6 𝑥
You try: write the exponential from the point given
0,1 𝑎𝑛𝑑 2, 49
0, 3 𝑎𝑛𝑑 2, 12
1, (4, 72)

11. Solutions 𝑦= 5 𝑥 𝑦=3 ∗ 2 𝑥 Hmmm how do we do that one by hand?
We get stuck with 9=𝑎∗ 𝑏 1 𝑎𝑛𝑑 72=𝑎∗ 𝑏 4

12. Steps to do it in the calculator given points/ data
Stat → Edit → 𝑒𝑛𝑡𝑒𝑟 𝑑𝑎𝑡𝑎 𝑖𝑛 𝐿 1 𝑎𝑛𝑑 𝐿 2 𝑆𝑡𝑎𝑡 →𝐶𝑎𝑙𝑐→𝐸𝑥𝑝𝑅𝑒𝑔 𝑦=𝑎∗ 𝑏 𝑥 𝑎=𝑠𝑜𝑚𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑏=𝑠𝑜𝑚𝑒 𝑛𝑢𝑚𝑏𝑒𝑟

13. Recall parent function Transformations
If we had the function 𝑦= 𝑥 2
How did we describe the transformation(s):
𝑦= 𝑥−3 2
𝑦= 𝑥 2 +4
𝑦=− 𝑥 2
𝑦= −𝑥 2

14. The same translations apply to exponential functions
We can use the characteristic point we know for exponentials to help use I.D. graphs
The point is 0,1

15. Examples
𝑦= 2 𝑥 𝑝𝑜𝑖𝑛𝑡 𝑜𝑛 𝑡ℎ𝑒 𝑔𝑟𝑎𝑝ℎ 𝑖𝑠 0,1 𝑎𝑛𝑑 2,4 If we transform the graph: 𝑦= 2 𝑥+1 the graph has been shifted one unit to the left so instead of 0,1 𝑡ℎ𝑒 𝑝𝑜𝑖𝑛𝑡 𝑖𝑠 𝑛𝑜𝑤 −1, 1

16. Try it
𝑦= 2 𝑥
Describe the translation(s) use the point 0,1 as a reference.
𝑦= 2 𝑥 +3
𝑦=− 2 𝑥
𝑦= 2 −𝑥
𝑦= 2 𝑥−3 +4