Question

Write the exponential equation that contains the points (−1,40)
and (2,1.08)
.(1 point)

Answer 1

Let y = a b^x. From the points:

1) x = −1: a b^(−1) = 40 → a/b = 40 → a = 40b
2) x = 2: a b^2 = 1.08

Substitute a: (40b) b^2 = 1.08 → 40 b^3 = 1.08 → b^3 = 0.027 → b = 0.3.

Then a = 40(0.3) = 12.

So the exponential equation is y = 12(0.3)^x.