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").
Answer:
it would be 5,000
Step-by-step explanation:
With digits 8, 5, and 6, an odd number must end in 5.
So far, we have _ _ 5.
The 8 is in the hundreds place.
Now we have 8_5.
The only place left for the 6 is the tens place.
The number is 865.
Answer:
The new volume is 4 times the old volume ♡
Hi there!
There are 3 parts to this equation:
f(x)
f(x+1)
4f(x)
We must first determine these three parts separately.
<u>1) f(x)</u>
We're given that 
:
⇒ :
<u>2) f(x+1)</u>
Now, we must find f(x+1). To do so, add 1 to x in the original function :
⇒ 
<u>3) 4f(x)</u>
To find 4f(x), multiply the original function by 4:
:
<u>4) Put it all together</u>
Now, plug each of the three parts into the equation :
Factor the left side
Divide both sides by 3^x
Because this equation is true, is therefore true.
I hope this helps!
