Question

How do you write an exponential equation that passes through (0,3) and (2,6)?

Answer 1

`f(x) = 3(sqrt(2))^x`

Explanation:

Suppose the required function is `f(x) = a*b^x` with `b > 0`

We are told `f(0) = 3` and `f(2) = 6`

So `3 = f(0) = a*b^0 = a*1 = a`

And `2 = 6/3 = f(2)/f(0) = (a*b^2)/(a*b^0) = b^2`

So, since `b > 0`, we must have `b = sqrt(2)`

Putting these together, `f(x) = 3(sqrt(2))^x`