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, 6, right bracket(0,6) and left bracket, 3, comma, 3072, right bracket(3,3072).
To find the exponential function that goes through the points (0, 6) and (3, 3072), we can use the general form of an exponential function: y = ab^x.
First, substitute the coordinates of the first point (0, 6) into the equation:
6 = ab^0
6 = a
Therefore, a = 6.
Next, substitute the coordinates of the second point (3, 3072) into the equation:
3072 = 6b^3
Now, solve for b. Divide both sides of the equation by 6:
512 = b^3
Take the cube root of both sides:
b = ∛512
b = 8
Now we have both values for a and b. The exponential function in the form y = ab^x is:
y = 6 * 8^x