Question

On a coordinate plane, an exponential function has a horizontal asymptote of y = 0. The function goes through points (negative 2, two-ninths), (negative 1, two-thirds), (0, 2), (1, 6), (2, 18), and (3, 54).
What is the multiplicative rate of change for the exponential function graphed to the left?

Answer 1

The function is y = 2·b^x (since y(0)=2). Using y(1)=6 gives 2·b = 6 so b = 3.
Thus the multiplicative rate of change is 3 (each x-step multiplies y by 3).