How to write an exponential function in the form y=ab^2

Question

The points are 0, 19 and 2, 171

Answer 1

(0,19) and (2,171) are points on an exponential curve

y =ab^x

plug in one point (0,19) x=0, y=19

19 =a(b^0) = a(1) =a

a =19

plug in the other point (2,171), x=2, y=171

y = ab^x

171 = 19b^2

b^2 = 171/19

b =sqr(171/19)

= 9

b=sqr9 = 3

y = f(x) = 19(3^x)

Answer 2

y = ab^x; 19 = ab⁰; a = 19; y = 19b^x; 171 = 19b²; b² = 9; b = 3; y = 19·3^x