Exponential translations

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

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

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

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

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

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?

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.

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.