Question

The graph of y = Ab^x, where A and b are

constants, passes through (2, 2) and
(5, 16). Find the value of A and of b.

Answer 1

A = 1/2, b = 2

Explanation:

Inputting (x, y) into y = Ab^x we know that

point (2, 2):

2 = Ab^2

point (5, 16):

16 = Ab^5

So:

16/2 = Ab^5 / Ab^2

8 = b^3

b = 2

Now inputting point (2, 2) with b = 2

2 = A*2^2

2 = 4A

A = 1/2