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

1 Answer
Jul 11, 2015

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