Algebra 2 question- logarithms

Question

Find an exponential funtion of the form y=ab^x whose graph passes through the points (2,1) and (3,2).

Answer 1

y = ab^x

 

[e1]   1 = ab²

 

[e2]   2 = ab³

 

Divide equation [e2] by equation [e1].

 

2 = b

 

[e1] ⇒ 1 = a(2)² = 4a

 

a = 1/4

 

y = (1/4)2^x

 

Test the answer against the given data.