Find the model for y = ab^x if (−1, 6) and (1, 8/3) are on the graph of the function.

Answer 1

f(-1)*f(1) = ab^-1*ab¹ = a²b⁰ = a²

f(-1)*f(1) = 6 * 8/3 = 48/3 = 16

a² = 16

a= ±4.

Since f(1) is positive, a = 4

f(1) = ab¹ = ab = 8/3

a = 4

4b = 8/3

b = 2/3

y = 4*(2/3)^x