124k views
0 votes
Determine the factor by which f(x) grows over the interval from 8 to 11 . f(x)=9^(x)

User LuckyLikey
by
7.9k points

1 Answer

5 votes

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.

User Slanecek
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories