Exponential Function

Question

Determine an exponential function in the form y=Cb^x given two points (0,-2) and (1,-6)

 

the answer is y= -2(3^x) but I do not know how that was reached

 

thank you in advance

Answer 1

y = Cb^x

 

Since (0,-2) is on the graph, -2 = Cb⁰.  So, C = -2.

 

Therefore, y = -2b^x

 

Since (1,-6) is on the graph, -6 = -2b^1.  So, b = -6/(-2) = 3

 

Thus, y = -2(3)^x