Question

How do you find an exponential function of the form f(x)=ab^x that has the given y-intercept (0,2); passing through P=(-1, 2/5)?

Answer 1

We know the value of `(x, y)` in two different cases. Therefore, we need to find the value of a and b. We have enough information to write a system of equations and to solve for a and b.

Explanation:

`2/5= a xx b^(-1)`

`2 = a xx b^0`

`2 = a xx 1`

`2 = a`

`2/5 = 2 xx 1/b`

`2/5 = 2/b`

`b = 5`

The equation of this function is therefore `y = 2 xx 5^x`.

Hopefully this helps!