Answer:
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").
Yes here is an example:_
x/4 + 5/6 = 2
The LCD of 4 and 6 is 12 but we can also multiply through by 24 to clear the fractions:-
x/4 * 24 + 5/6 * 24 = 2 + 24
6x + 20 = 40
This will give us the same result if we multiplied through by 12.
ANSWER
EXPLANATION
We want to evaluate
Use indices to rewrite the expression as:
We know that
So we rewrite the expression to obtain;
This gives us;
This simplifies to
See the photo attached. The boxed answer is the corrected answer
