Write an exponential function in the form y=ab^xy=ab x that goes through points (0, 2)(0,2) and (3, 686)(3,686).

Y = a b^x

find the values for a and b :

1- you have the point (0,2)

Substitute 0 for x and 2 for y

2 = a * b ^0
2= a * 1
a= 2

2- you have the point (3,686)

Substitute 3 for x and 686 for y and 2 for a

y = 2 b^x

686 = 2 * b^3

343 = b^3

b = 7

y = 2 * 7^x