please help with my math

Question

write an exponential function of the form y=ab^x that includes the given points:

1.) 2.)

(1,2),(2,8) (-1, 2/9), (1,2)

Answer 1

I will do the first one; you do the second one using the same reasoning.

(1)

y = ab^x

From the first point, equation 1:

2 = ab¹ = ab

From the second point, equation 2:

8 = ab²

Divide equation 2 by equation 1 and get

4 = b

Plug the result for b into either equation to find a.

8 = a(4²) = 16a

a = 1/2

b = 4

y = (1/2) 4^x

Test the answer.