exponential equation 2!

Question

Write an exponential equation that goes through the points (2, 12) and (5, 96)

Answer 1

f(x) = C * b^x

(2,12) ---> f(2) = 12 ---> 12 = C * b^2

(5,96) ---> f(5) = 96 ----> 96 = C * b^5

But 96 = 12 * 8

C * b^5 = 8 * C * b^2

b^5 = 8 * b^2

b^3 = 8

b = 2

Per first equation: 12 = C * b^2

12 = C * 2^2

12 = 4 C

C = 3

f(x) = 3 * 2^x