1. Exponential translations

2. Exponential Translations
y = a∙bx-h+k -h +k
h tells us how the function moves left or right (don’t forget that h is being subtracted!)
k tells us how the function moves up or down

3. Example 1
Describe the translation (initial value, growth or decay factor, and vertical and horizontal translations): y = 2∙4x-6-5

4. Example 2
Describe the translation (initial value, growth or decay factor, and vertical and horizontal translations): y = -3∙2x+2+4

5. Example 3
How would the function y = 3∙4x be written if it was translated down 2 and right 7?

6. Example 4
How would the function y = 5∙2x be written if it was translated left 3 and up 9?

7. Exponential Regression
What if we are given a graph or data that looks like it has an exponential trend? How do we find an equation for it?

8. Exponential Regression Steps
Enter the data into L1 and L2. (STAT → Edit…)
Use the ExpReg tool. (STAT → CALC)
Substitute the value for a and b into the equation y = a(b)x.

9. Time (mins)   
Temp ( ° F)   
179.5 5
168.7 8
158.1 11
149.2 15
141.7 18
134.6 22
125.4 25
123.5 30
116.3 34
113.2 38
109.1 42
105.7 45
102.2 50
100.5
The data at the right shows the cooling temperatures of a freshly brewed cup of coffee after it is poured from the pot.  The pot’s temperature is approximately 180° F. Find an exponential regression model for the data.