Find a formula for the exponential function passing through the points (-1,2/3 ) and (2,18)

Answer 1

2/3 = ab^-1

18 = ab²

27 = b³, divide bottom equation by top equation.

3 = b

18 = a(9)

2 = a

y = 2(3)^x

Answer 2

y = a(b)^x

Since (-1, 2/3) is on the curve, 2/3 = a(b)^-1

So, a = (2/3)b

y = (2/3)b(b^x)

Since (2, 18) is on the graph, 18 = (2/3)b³

So, b³ = 27. Therefore, b = 3 and a = (2/3)(3) = 2.

So, y = 2(3)^x