rate of change

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[lament knot]

i'd like to know what formula to use for this question, also please ping me once you respond, thank you :)

[gritty ivy]

Rate of change is the amount of change per some amount of time, i.e., just the slope

[lament knot]

so what formula shoudl i use

im quiet confused

[gritty ivy]

No formula needed from t=8 to 10, because the graph is linear. Just find the slope

[lament knot]

should i use delta y/delta x

oh

how do i do that, i forgot how to do that 😭

[gritty ivy]

"delta y/delta x", "rise over run", etc.

[lament knot]

ah okay

so when i do it

i just plug in

x2-x1/y2-y1

[gritty ivy]

Yeah

[lament knot]

wow i really made things complicated for myself

thank you so much

so the answer should be 1

[gritty ivy]

No, try again

[lament knot]

before simplifying it

ohh

i did it wrong

okay

one moment

[gritty ivy]

As an exercise, try finding the average rate of change between t=4 and t=10. And what about between t=0 and t=10?

[lament knot]

formula should be y1-y2/x1-x2, correct?

[gritty ivy]

Yes

[lament knot]

the answer is 2/2

[gritty ivy]

No

[lament knot]

huh

what am i doing wrong

[gritty ivy]

What is 5-2

[lament knot]

-2

😭

I FORGOT

THANK YOU

so -2/2

[gritty ivy]

No

[lament knot]

eaiy

-3

my bad

[gritty ivy]

What is 5-2

[lament knot]

my brain isnt working

its -3

[gritty ivy]

I guess you're using the formula?

[lament knot]

huh

im usig the formula

[gritty ivy]

What is 5-2

[lament knot]

3

just 3

3/2

[gritty ivy]

Yes. Now what is 10-8?

You got it!

[lament knot]

2

yay!!

ill try the excersize you gave me now

[gritty ivy]

Now try this.

[lament knot]

-10/-6

but if you simplify it, it should be -5/-3

and two negatives make positive

so 5/3

[gritty ivy]

Between t=4 and 10?

[lament knot]

oh

i wrote 0

instead of ten

sorry

wait

4-10 is -6

did i do it wrong

[shy swift]

@lament knot

Remember slope formula from algebra 1?

(y2-y1)/(x2-x1)

That's all it is

So go to the interval (meaning what number on the x axis) it's asking for

Plot the beginning interval, to the end interval

Those are your two points

Plug into slope formula

Solve

[lament knot]

for the graph or the excersise i was given?

[shy swift]

The interval it's asking for

An interval is just a piece of the x axis aka seconds in this instance

[lament knot]

ah so this isnt what i was supposed to do?

[shy swift]

Okay man

What's the x axis

Tell me what an x axis is and a y axis

[lament knot]

sorry

[shy swift]

Here

Let me see if this helps

[lament knot]

x is horizontal y is verticle

[lament knot]

thank you

[shy swift]

So

What's the x and y of the first point it asks for

[lament knot]

2

(8,2) (5,10)

[shy swift]

That's wrong

first interval is right, second is wrong

Try again,

Remember x goes first, y comes second

[lament knot]

ohh

sorry

[shy swift]

nah you're good

[lament knot]

(8,2) (10,5)

[shy swift]

Now what was the slope formula we talked abt

[lament knot]

i havent been sleepign well recently so its catching up to me

y1-y2/x1-x2

[shy swift]

Almost

[lament knot]

ah

[shy swift]

uh

[lament knot]

y2-y1/x2-x1

[shy swift]

yes that's correct

[lament knot]

i thought you can do both way

[shy swift]

Nah

[lament knot]

i remember being told that

[shy swift]

I mean maybe? But I don't recommend it

[lament knot]

so if i plug it in it'll be

3-5/8-10

[shy swift]

no

The first point was the first ordered pair i.g (8,2)

[lament knot]

ohhh

[shy swift]

Because that's how the question is ordered

from 8 TO 10

[lament knot]

idk where 3 came form

[shy swift]

Meaning 8 comes first, 2nd is 10

[lament knot]

okay so 2-5/8-10

[shy swift]

Still, no

Remember 2nd is subtracted first

y2-y1

Not y1-y2

1st pair being (8,2) 2nd pair being (10,5)

[lament knot]

i have to wirte it down on paper

[shy swift]

That's fine

I'd recommend it when starting algebra

Dw tho in a couple more of years of this you'll just start recognizing the slope in like 10 seconds of staring at 2 points

[lament knot]

im in grade 12 😭

[shy swift]

Tf

[lament knot]

i just have horrible memory

[shy swift]

Aw hell

[lament knot]

I JUST NEED A REFRESHER

[shy swift]

I'm in grade 12 and my equations be like

on some bs

[lament knot]

r u doing adv funcitons or calc

or data management

[shy swift]

Calc

[lament knot]

ok that makes sense

im doign advacned fucntions

[shy swift]

Huh this seems easy

[lament knot]

and this unit goes back to grade 9

[shy swift]

I wonder if yall will touch algorithims

Yeahhhhh I can see that

[lament knot]

the unit before was worse

[shy swift]

Basically I took algebra 1, algebra 2, geometry, and precalc

[lament knot]

and its just one quesiton form my assigment so its easy

[shy swift]

sadly precalc only reviewed like

6 weeks of algebra 2

And we got so much shit to cover

[lament knot]

are you american?

[shy swift]

Yup

[lament knot]

okay yeah that makes sense

im canadain

so

[shy swift]

Bro you need all the way up to algebra 2 to graduate

Basically algebra 1 is abt lines and graphing and all that

[lament knot]

we just have grade 9 and 10 math, functions, advanced functions, data management and calc

aperently theres another one too

[shy swift]

Algebra 2 is abt functions, quadratics, other stuff,

Geometry is yk

[lament knot]

is this grade 9 math

[shy swift]

Yeah Algebra is grade 9 math

And what we're doing rn isn't even algebra tbh

It's more like intermediate

[lament knot]

oh okay

[shy swift]

Did you write the problem down btw?

[lament knot]

yes i did and i still got 2-5/8-10

[shy swift]

Okay

1st pair is (8,2)

2nd pair is (10,5)

[lament knot]

i feel bad, after advanced functiosn im done math (until uni)

[shy swift]

x1=8

x2=10

[gritty ivy]

This isn’t wrong

[lament knot]

ikm confused then

[gritty ivy]

For the slope between t=8 and 10

[shy swift]

Why doesn't he just do it y2-y1/x2/x1

[lament knot]

she 😭

[gritty ivy]

It’s the same

[shy swift]

Is that a candadian thing?

OH

My fault

[lament knot]

😭

[shy swift]

Ik

Negatives cancel out

Still end up with answer

[shy swift]

nyways yes what's the answer once you do it like that 😔

Still sad you didn't plug it in My way-Frank Sinatra ™️

[gritty ivy]

She already did the problem given in the hw

[shy swift]

💀

[lament knot]

would you like me to do it yoru way

[gritty ivy]

It makes no difference

[shy swift]

Because it's just cooler and less steps

Or step

[gritty ivy]

The important thing here isn’t memorizing a formula the right way. You need to understand the concept of slope, regardless of which formula you use

[shy swift]

since then you don't gotta cancel it

I mean the formula is p simple

I'd be more worried abt

Point slope

Slope intercept

Standard/General form

[lament knot]

okok i understand it i jsut kidn of have probnlems of when i use a formula

[lament knot]

how ocme

also would it be okay if i ask for more help

[shy swift]

They're confusing imo

They all sound the same

and ofc

I'm not even a helper

Urgle is

If you ever appreciate someone helping

You can nominate them in a channel lol

[lament knot]

urgle is amazing

i will

[shy swift]

Go nominate em

#helper-nominations

[gritty ivy]

Those are just more formulas to memorize, and the more important thing is understanding what pieces of information distinguish a line

[shy swift]

OH and they almost always intertwine within questions

Sometimes you gotta go from one to the other to the standard (something like taht I lowkey forgot it's been a long long while)

[lament knot]

are they all plugging in

[lament knot]

😭

wait

i think i did slope intercept

i cant remember id have to se a picture

anyway im droppign another question in if that is okay

for this i a(t)=100 (1.04)^t as the formula so i basicalluy wrote 100(1.04)^18

is that correct

i got my final answer to be 202.5816

[shy swift]

Okay

So yeah that'd be correct

You plugged in 18 for t

which is marie's age

[lament knot]

ok

ikm glad

i keep thinking im doing it wrong

[shy swift]

Uh

This ain't right tho

[lament knot]

uh oh

[shy swift]

Some how

😭

[lament knot]

maybe i just did it all at once

let me try again

[shy swift]

Wait

Uh

By calculator tripping mb

[gritty ivy]

This is asking for instantaneous rate of change, so you need the derivative of A at t=18

[lament knot]

scared me

[shy swift]

😭

[lament knot]

okay, so basically just plugging it in

[gritty ivy]

But it says “estimate”. Try to find the slope between A(17.9) and A(18.1)

[gritty ivy]

For the exact answer, after you differentiate A with respect to t

[lament knot]

oh so just at 18, right?

[gritty ivy]

This is the amount of money. The problem is asking for the rate of change of the money

[gritty ivy]

No, you need two points to find a slope

[lament knot]

i have to graph it?

[gritty ivy]

Which is why you can try two points very close to A

[gritty ivy]

No, just find the difference between A(17.9) and A(18.1) and divide it by 0.2

[lament knot]

how do i find the difference between A(17.9) and A(18.1)

[gritty ivy]

Find A(17.9). Next, calculate A(18.1). Finally, take the difference between those two values

[lament knot]

i apologize

i am so sorry

i do not undertsant

do i just plug it in

[gritty ivy]

No problem, take it step by step. What is A(17.9)?

[lament knot]

into the formula

[gritty ivy]

Yes, plug t=17.9 into A(t)

[lament knot]

a(17) is her age, right?

[gritty ivy]

No, t is her age. A(t) is the money she has at that age

[shy swift]

[lament knot]

oh ok so what i do is i make a seprate equation for both a(17.8) and one for a(18.1)

[lament knot]

[gritty ivy]

Yes, find those two values separately

[lament knot]

so i will write a(17.9)=100(1.04)^18?

for teh first one

[gritty ivy]

No, you want the exponent to be 17.9. Because that’s what t is

[lament knot]

so a(18)=100(1.04)^17.9

[gritty ivy]

A(17.9), not 18

[lament knot]

a(17.9)=100(1.04)^17.9

[gritty ivy]

Yes. After you find that value, do the same with 18.1

[lament knot]

oky, i will solve that right now

[lament knot]

i got 201.7886

now ill start 18.1

a(18.1)=100(1.04)^18.1 = 203.3777

[gritty ivy]

203.3777-201.7886=?

[lament knot]

ok so i have to subtract those too

those two

[gritty ivy]

Yep. Going back to the formula, this is like the “delta y”

[lament knot]

ok that makes sense

i got

1.5891

[gritty ivy]

Ok, now divide that by 0.2. Remember, that’s like the “delta x”

[lament knot]

7.9455

[gritty ivy]

Ok, so that’s our estimate

[lament knot]

is that the full quesiton

[gritty ivy]

Yeah, it’s only asking for an estimate. It doesn’t specify the level of precision we need, so I guess 7.9455 thousand dollars per year is a decent estimate

[gritty ivy]

Would you like to see how close the estimate was to the exact rate of change?

[lament knot]

yes please

[lament knot]

ohh okay okay

[gritty ivy]

First we need to find A’(t). Using the rule giving the derivative of an exponential function, we get A’(t) = 100 * 1.04^t * ln(1.04)

[lament knot]

what is ln

[gritty ivy]

Natural log; in calculus this is log base e

[lament knot]

i dont think my calculator has a log

[gritty ivy]

This rounds to 3.9221 * 1.04^t. Plugging in 18, we get 7.9454

So our estimate was pretty close

[lament knot]

only one number off

[gritty ivy]

Yep

[lament knot]

am i keeping you up?

[gritty ivy]

Not really, but I will sleep soon

[lament knot]

please do, thank you so much for the help i really appericate this

[gritty ivy]

Np, if u want to learn more about rate of change/calculus, I recommend khan academy

[lament knot]

okay, ill try that out

also

does it help for university math

or does it stop at highschool

[gritty ivy]

Calculus is “university math”, but I think it also does offer some diff eq and linear algebra. Not sure tho

But it is pretty high quality teaching imo

[lament knot]

but calculous is also grade 12 math

maybe its just a canadian thign idk

[gritty ivy]

I wouldn’t worry about what grade the material is considered to be tbh, it’s not important at all

If u find it interesting, u definitely should study it

[lament knot]

well i might nto until university since i dont think i need grade 12 calculous

wow i never knew that really

[gritty ivy]

Ah I see. In ur case I think it wouldn’t hurt at all to begin studying calc, but it would likely take quite a lot of effort

It’s fine to wait until uni

[lament knot]

yeah it woule be best for me

to study earlier