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NationalTutoringObservatory
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MathEd-PII

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student
im confused on how to do this one
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volunteer
This one is interesting
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volunteer
Do you know the formula for average rate of change?
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student
y=x??
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student
or is it f(b)-f(a)/b-a
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volunteer
The second one
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volunteer
The first one you listed I believe is the slope intercept form of a linear equation
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student
ohh okay!!
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student
so how would I go about plugging the equation into the formula?
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volunteer
So this is a trick question but theres some reasoning behind it
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volunteer
The f(20)-f(10) / 10 is actually a rate of change formula since 10 can be rewritten as 20-10
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volunteer
and f(20)-f(10) / 20-10 matches f(b)-f(a) / b-a
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volunteer
So the question is effectively asking for the rate of change of f
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student
by plugging that into the calculator I got an error, did I do it wrong??
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volunteer
The question doesn't need a calculator since the answer is already in the question
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student
and the answer is the last one correct??
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volunteer
Well
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volunteer
The slope (or rate of change) of a linear function is the same across the entire function
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volunteer
So if the slope of f is 12/5 for one interval its 12/5 for all other intervals
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volunteer
And f(20) - f(10) / 20-10 is the rate of change of f across the interval [10, 20]
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volunteer
uh
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volunteer
The question is asking for the rate of change, not the interval
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volunteer
And the rate of change across the entire function is 12/5
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student
this may be silly but would you mind solving an example problem similar to this one for reference
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student
I wasn't sure that was the correct answer, but the way I read the message made it sound like that it was obviously simple lol
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volunteer
Alright sure
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volunteer
So lets say the rate of change of a linear function a is 4 across the interval [0, 1]
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volunteer
And you have to calculate the rate of change of function a across a different interval
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volunteer
regardless of what that interval is the rate of change will always be 4
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volunteer
so basically f(b)) - f(a) / b-a = 4 no matter what
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volunteer
as long as youre solving for something in that form for a function the answer will always be the rate of change
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volunteer
so in this case since f(20) - f(10) / 20-10 is the right form for rate of change
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volunteer
it will equal 12/5 since thats what the rate of change is for the entire function
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volunteer
if that makes sense
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student
okay yes that makes sense
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student
so the entire thing equals 12/5
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volunteer
Yes its 12/5
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volunteer
Do you need help with this one?
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student
yes please :)
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volunteer
Casey
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[ { "pii_type": "PERSON", "surrogate": "Casey", "start": 0, "end": 5 } ]
volunteer
Could you try zooming into the question my eyesight is horrendous
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student
oh lawd yes I can
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student
tell me if I need to move it
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volunteer
Ok so this question is asking for if the rate of change is staying constant across the range of values
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volunteer
Are you allowed to use a calculator for this question?
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student
yes
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volunteer
Graphing or scientific?
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student
im not sure
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student
I assume graphing
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student
??
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volunteer
Basically what you have to do here is use the equation for rate of change
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volunteer
for two pairs at a time
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volunteer
Each pair is a number of servings and the total cost for that number of servings
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student
how would I put it into the calculator
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volunteer
What model of calculator is it
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volunteer
If its not a ti84 I genuinely have no idea how to use it
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student
im using the gauth calculator
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student
I dont have one of my own
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student
other than at school
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volunteer
Oh
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student
yep...
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volunteer
Unfortunate
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volunteer
Theres a method you can use with the ti84 to cheese these types of questions
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student
if you were to set it up how would it look though
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student
like would you set it up as a fraction
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volunteer
To do it properly you basically have to calculate f(x2)-f(x1)/x2-x1
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volunteer
and then another calculation
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volunteer
and so on
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volunteer
because that calculates the rate of change between each pair
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volunteer
Im gonna do it myself just to make sure
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student
do you have the right type of calculator
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volunteer
Any calculator works
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volunteer
If we do it the proper way that I described
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volunteer
The fast method only works with the ti84 so we won't be using that
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student
the answer to the first calculation is 4.65 correct??
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volunteer
For the rate of change between the first two pairs yes thats correct
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volunteer
Now you have to calculate the rate of change between (5, 33.24) and (9, 49.81)
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volunteer
so f(9)-f(5)/9-5
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volunteer
and then after that you have to do the rate of change between (9, 49.81) and (11, 57.96)
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volunteer
its a long process
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student
would the answer be 4.075
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volunteer
Well the question is asking for if the rate of change is increasing, decreasing, or staying the same
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volunteer
So you have to compare the rates of change between the points
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volunteer
So if the rate of change is changing from 4.65 to 4.075 then that means its decreasing
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student
okay so the rate of change is decreasing while the number of servings is increasing
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volunteer
As the number of servings increase, the rate of change decreases yes
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student
what's the difference between quadratic and linear
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volunteer
Theres multiple differences
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volunteer
Linear equations are mostly in the form y = mx + b
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volunteer
but quadratic equations are in the form y = ax^2 + bx + c
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student
how could I tell which one it is by just looking at h
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volunteer
By looking at differences
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volunteer
Basically find the difference between each value of h
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volunteer
so between 18 and -12
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volunteer
and then -12 and -29
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volunteer
and -29 and -33 and so on
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student
are they all supposed to follow a pattern
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volunteer
Yes
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volunteer
if they are all equal the function is linear
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volunteer
If the differences of the differences are equal then the function is quadratic
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