Question

Find a formula for an exponential function passing through the two points.
(0,2) and (5, 64)

Answer 1

y = 2(2^x)

The exponential function will take the form y = a(b^x), so we need to find the values of the constants a and b by subbing in our two points to get simultaneous equations:

2 = a(b^0)
As anything to the power of 0 (apart from 0) is 1, then we can immediately find that a = 2

With the second point, 64 = 2(b^5)
32 = b^5
Hence b = 2
Now we can rewrite the equation with the values for a and b.