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: x=0
Step-by-step explanation:
The line has an undefined slope and has infinitely many solutions as it passes through the y-axis
Therefore the equation of the line is x=0
Answer:
The rate is the distance divided by the time.
60 feet in 10 seconds = 60 ft / 10 sec = 6 ft / sec
42 feet in 6 seconds = 42 ft / 6 sec = 7 ft / sec <--- We have a winner!
Step-by-step explanation:
<span>The shortest path from a starting point to an endpoint, regardless of the path taken, is called the </span>geodesic. In flat (Euclidean) space it is simply a straight line.
So first you want to convert both to have the same denominator.
5 1/2 - 3 3/4
To:
5 2/4 - 3 3/4
Now, to make it easier for me, I would convert both to an improper fraction.
5 2/4 -> 22/4
3 3/4 -> 15/4
So now you can just do,
22/4 - 15/4,
which is just 7/4.
This in mixed number form is 1 3/4.
