Question

How do you find an exponential function of the form `y=ab^x` whose graph passes through the points (2,1) and (3,2)?

Answer 1

`a = 1/4 and b = 2`. And so, `y = 2^x/4`..

Explanation:

On a semi-log (x vs Y=log y) the graph of `y = a b^x` will be a

straight line for Y = log y = log a + x log b#.

Substituting (x, y) = (2, 1) and (3.2), we get

`0 = log a + 2 log b and log 2 = log a + 3 log b`.

So, `a = 1/4 and b = 2`.