Question

How do you find formulas for the exponential functions satisfying the given conditions h(0)=3 and h(1)= 15?

Answer 1

An exponential function is a function of the form `y = ab^x`.

Knowing the inputs and outputs of the function, we can write a systems of equations, with respect to `a` and `b` to represent the problem.

`3 = ab^0`
`15 = ab^1`

The simplest way of solving this system will be using the fact that `n^0, n in RR = 1`. So, we immediately know that `a = 3`.

We insert `a = 3` into the second equation to get `b = 5`.

So, the exponential function is `y = 3(5)^x`.

Hopefully this helps!