Write an exponential function in the form y, equals, a, b, to the power x y=ab

Question

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).

Answer 1

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