Question

How do you find an exponential function of the form f(x)=ab^x that has the given y-intercept (0,5); passing through P=(2, 5/9)?

Answer 1

`f(x)=5(1/3)^x.`.

Explanation:

`f(x)=ab^x, b>0`.

#f(0)=a(1)=5.

`f(2)=5b^2=5/9`.

So, `b^2=1/9`.

`b=+-1/3`. Negative root is inadmissible.

So, `b = 1/3`..