What exponential function is the best fit for the data in the table?

x f(x)

2 -3

3 0

4 12

f(x)=4(4)^(x-1)+4
f(x)=4(4)^(x-1)-4
f(x)=1/4(4)^(x-1)+4
f(x)=1/4(4)^(x-1) -4

look at the picture.

y-intercept for the function on a picture is 4 → point (0, 4).

y-intercept for the function

is for x = 0. substitute:

y-intercept is 8 → point (0, 8).

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like:

more information !