write an exponential function with two given points

Question

Write an exponential function in the form y=ab^xy=abx that goes through points (0,9) and (3,4608).

Answer 1

Just take the basic form y=ab^x and plug in the two points (0,9) and (3,4608):

First:

9 = ab⁰

9 = a(1)

a = 9

Second, now that you know what "a" is:

y = 9b^x

4608 = 9b³

4608/9 = b³

512 = b³

b = cuberoot(512) = 8

So:

y = 9(8^x)