College algebra

Question

Find the equation of the exponential function that passes through the points (0,1) and (2,9).

Answer 1

We use the coordinates to figure out an equation.  Since we need an exponential function, there will be an exponent in the function.  Exponential functions have curvature features when plotted on a coordinates system.

 

y = 3^x

Answer 2

Hello, thank you for taking the time to post your question!

The general from of an exponential function is given by the equation

y = a * b^(x)

since we’re given the point (0,1) directly that means that a = 1

so the equation can be simplified down to

y = b^x

from there then I would use the second point to find the value of b

9 = b^2

b = sqrt(9) = 3

meaning that the underlying equation here is

y = 3^x

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)