Final answer:
To calculate the growth factor of the function f(x) = 9^x from x = 8 to x = 11, evaluate the function at both points and divide f(11) by f(8) resulting in a growth factor of 729.
Step-by-step explanation:
To determine the factor by which the function f(x) = 9^x grows over the interval from x = 8 to x = 11, we must evaluate the function at these two points and then calculate the ratio of the two results.
We start by evaluating the function at x = 8:
f(8) = 9^8
Next, we evaluate the function at x = 11:
f(11) = 9^11
The growth factor over this interval is determined by dividing f(11) by f(8):
Growth factor = f(11) / f(8) = 9^11 / 9^8 = 9^3
Simplifying this, we find that the growth factor is:
729
Hence, the function grows by a factor of 729 over the interval from x = 8 to x = 11.