math exponential function of the form y = abx

Question

The graph of an exponential function of the form y = ab^x contains the points (2, 60) and (4, 240).

What are the values of a and b?

Answer 1

Use the 2 given points to solve for the 2 unknowns a and b.

60 = ab²

240 = ab⁴

Divide bottom equation by top equation and get

4 = b²

b = 2

Now plug the result for b into either equation to get a. Using the top equation,

60 = a (2)² = 4a

a = 60/4 = 15

y = 15 (2)^x

Test this answer against the given points.