Answer:
F(x) = 2 * 2^x
Step-by-step explanation:
To find an exponential function that fits the given values, we can use the general form of an exponential function:
F(x) = a * b^x
Given that F(3) = 16 and F(6) = 128, we can set up the following equations:
16 = a * b^3 (1)
128 = a * b^6 (2)
We can solve this system of equations to find the values of a and b.
Divide equation (2) by equation (1):
(128 / 16) = (a * b^6) / (a * b^3)
Simplify:
8 = b^3
Taking the cube root of both sides:
b = 2
Now, substitute b = 2 into equation (1) to solve for a:
16 = a * 2^3
16 = 8a
a = 2
Therefore, the exponential function that fits the given values is:
F(x) = 2 * 2^x
