Question

How do you find the exponential model `y=ae^(bx)` that goes through the points (0,4) and (5, 1/2)?

Answer 1

Solve for `a` using equation 1 and then for `b` using equation 2.

Explanation:

Basically we need to solve for both `a` and `b`. Since `x=0` in the first equation I know that the exponent will be `0` and anything raised to `0` is evaluates to `1` so let's do this first to easily solve for `a`.

`4=ae^(b0)`
`4=a×1`

Having the value of `a` we use the second equation to solve for `b`.
`1/2=4e^(b5)`
`1/8=e^(b5)`
`ln(1/8)=b5`
`ln(1/8)/5=b`