Given the function f(x)=4(2)2, Section A is from x=1 to x=2 and section B is from x=3 to x=4. Part A: find the average rate of change of each section. Part B: How many times greater is the average rate of change of section B than section A? Explain why one rate of change is greater than the other.

I found thois from someone else asking this queetion so gope it helps.

Step-by-step explanation:

I'm sure you want your functions to appear as perfectly formed as possible so that others can help you.  f(x) = 4(2)x should be written with the " ^ " sign to denote exponentation:  f(x) = 4(2)^x

                                                                                     f(b) - f(a)

The formula for "average rate of change" is a.r.c. =

                                                                                          b - a

                                   change in function value

This is equivalent to  

                                           change in x value

For Section A:  x changes from 1 to 2 and the function changes from 4(2)^1 to  4(2)^2:  8 to 16.  Thus, "change in function value" is 8 for a 1-unit change in x from 1 to 2.  Thus, in this Section, the a.r.c. is:

                8

              = 8 units    (Section A)

                 1

Section B:  x changes from 3 to 4, a net change of 1 unit:  f(x) changes from

4(2)^3 to 4(2)^4, or 32 to 256, a net change of 224 units.  Thus, the a.r.c. is

       224 units

      = 224 units (Section B)

           1 unit

The a.r.c for Section B is 28 times greater than the a.r.c. for Section A.

This change in outcome is so great because the function f(x) is an exponential function; as x increases in unit steps, the function increases much faster (we say "exponentially").

answer: 1 + 1 = 11

step-by-step explanation:

i believe the correct answer is option 4.principalities were small territories that were run by russian rulers.

which statement correctly defines principalities in northern asia in the 1200s? principalities were small territories that were run by russian rulers.

hope i could ! : )