Write an exponential function in the form y, equals, a, b, to the power x y=ab
x
that goes through the points left bracket, 0, comma, 3, right bracket(0,3) and left bracket, 2, comma, 243, right bracket(2,243).
To find the exponential function in the form y = ab^x, we need to find the values of a and b.
Given the point (0,3), we can substitute these values into the equation:
3 = a * b^0
3 = a * 1
a = 3
Therefore, our equation becomes y = 3 * b^x.
Now, let's substitute the values of the second point (2,243) into the equation:
243 = 3 * b^2
b^2 = 243/3
b^2 = 81
To solve for b, we take the square root of both sides:
b = √81
b = 9
Now we have the values of a = 3 and b = 9, so the exponential function that goes through the points (0,3) and (2,243) is:
y = 3 * 9^x