Question

An exponential function has the form f(x)=b to the power x why b>0

Answer 1

In the form f(x) = b^x, It is not necessary that b>0. b can be both greater than and less than 0. But it can't be 0 because then f(x) will be 0 which is not a exponential function.

Answer 2

Exponential function : $f (x) = b^x$

Examples of some exponential functions are : 
$e^x, 2^x, 3^x,  10^x, e^{-x}, 10^{-x},$

Generally they are studied like that.  if b > 0, then b^x is > 0 and f(x) > 0.

b can be taken as negative also, where it is needed. But in general when we talk about exponentially increasing function it is e^x and when it is exponentially decreasing we use e^-x.

If b = 0, then f (x) = 0, so it does not increase or decrease.