Exponential Function

Question

An exponential model y=a⋅b^x  passes through the points (0, 4) and (2, 36). What are the values of a and b ?

a=

b=

Answer 1

We are solving for y = ab^x

There is one less step when you are given the y-intercept, as a is the y-intercept (b^x = 1 for all b not equal to 0).

a = 4

Then, as the function goes through (2, 36), and y = ab^x, 36 = 4 * b²

b² = 36/4 = 9

b = 3 (while b = -3 would also work for these points, one normally just takes the positive solutions.

y = 4 * 3^x