Is this accurate?

[red venture]

looks ok

to me

[undone belfry]

Could you help me set up #4?

@red venture?

[burnt thorn]

#4 seems pretty simple, but ill do 4A as an example

,tex $A_n = 100(2^{n})$

[elfin schooner]

@burnt thorn

[burnt thorn]

,tex $A_2 = 100(2^{2})$

[elfin schooner]

@burnt thorn

[undone belfry]

So would b be A_=100(5^n)?

[burnt thorn]

close

[elfin schooner]

@burnt thorn

@burnt thorn

[undone belfry]

So n would be 2 for a, and n would be 5 for b?

[burnt thorn]

perfect

[undone belfry]

So all together, b would be a_n=100(2^5)?

[burnt thorn]

technically yes, but your teacher wouldnt accept

[undone belfry]

Why not?

[burnt thorn]

remember, n also exists in A_n

so you have to substitute the value of N

so it would be A_2, A_5, A_10

[undone belfry]

So how would I solve this showing work because it seems pretty self explanatory to me?

[burnt thorn]

small thing, but most teachers are picky

[burnt thorn]

yep, doesnt seem like there are any tricks

[undone belfry]

But in the directions, it says I must show work. Is there anything I can put here to show a little bit of work?

[burnt thorn]

of course

show that u substitute the variables

then show that you raised 2 to the nth power

then show that u multiplied the above result by 100

[undone belfry]

What is the original equation without substituting again?

[burnt thorn]

,tex Example: $A_4 = 100(2^{4}) = 100(16) = 1,600$

[elfin schooner]

@burnt thorn

[burnt thorn]

,tex $A_n = 100(2^{n})$

[elfin schooner]

@burnt thorn

[undone belfry]

No but what variable is 100 and what variable is 2? (Without plugging those numbers in to the equation?)

[burnt thorn]

didnt u write the equation

but anyways

[undone belfry]

Yes, I did.

[burnt thorn]

100 is how many people are at the stadium at hour 1

2 refers to the "common ratio of 2" which means that the amount of people multiplies by 2 every hour

[undone belfry]

Got it. I may need more help momentarily if you will be available.

[burnt thorn]

yeah sure, i have to go to sleep in 25 mins tho

[undone belfry]

Wait so would the amount of people in the stadium at hour 2 be 400?

[burnt thorn]

100(2^2) = 100(4) = 400 ✅

typing... 👀

[undone belfry]

Hour 10 being 102,400 people which I believe is correct if you would like to confirm. But question 5 says what hour will the attendees first pass half the maximum capacity. Well, 102,400 is way over the maximum capacity because 63,400 is the maximum. So what do I need to do to solve #5?

[burnt thorn]

it says "Using the formula above"

so i would assume that, for just #4, the attendance can be more than the capacity

[undone belfry]

I suppose.

[burnt thorn]

,tex $A_n = 100(2^{n})$, $A_n = \frac{63,400}{2}$

[elfin schooner]

@burnt thorn

[burnt thorn]

do you see where i got both of those equations for from?

[undone belfry]

So that’s the formula I need to use to solve #5?

[undone belfry]

I believe so.

[undone belfry]

Could you explain quickly just to make sure I understand fully?

I appreciate your help so far by the way.

[burnt thorn]

sry for late repsonse

so anyways

[undone belfry]

No worries.

I’m not sure too sure how to solve.

[burnt thorn]

the first equation is the equation that you wrote to represent the amount of people in the stadium.

the second equation says that the amount of people is equal to half of the maximum capacity

btw im purposefully keeping my explanations as basic as possible so that you will only ask help on what you don't understand

so please dont feel embarassed for asking

[undone belfry]

So would it be something like 31700=100(2^n)?

[burnt thorn]

yep

now you have to solve for n

[undone belfry]

The answer isn’t 177.76 right?

[burnt thorn]

and no, the answer is not ||8.30833903||

[burnt thorn]

no

but if u can explain how u got that, i can tell you where u went wrong

[undone belfry]

Is it 8.30?

[burnt thorn]

in reality, yes. but that would be the wrong answer to this question

the problem says "At what hour"

so they are technically asking for a whole hour

and we are not looking for an hour during which the attendance is exactly half the capacity, we only want the attendance to pass half the capacity

[undone belfry]

So what do I do to get that?

Now that I know that n=8.30.

[burnt thorn]

8.3 is not correct because that is not a whole hour

we have to find a whole hour where the attyendance passes half the capacity

still confused?

[undone belfry]

Not really, just on how to get the whole hour where the attendance passes half the capacity.

What do I need to do figure that part out?

[burnt thorn]

so we know that the exact answer would be 8.4

*8.3

so lets look for whole numbers that are around 8.3

[undone belfry]

8

[burnt thorn]

alr lets start with 8

at hour 8...

• what is the attendance of the stadium
• has the attendance passed have the capacity?

[undone belfry]

25600
Yes

[burnt thorn]

nope

[undone belfry]

Where do I plug 8 in?

[burnt thorn]

this time i wont explain because i know you will understand after you reread the original problem

[burnt thorn]

,tex $A_n = 100(2^{n})$, $n = 8$, $A_8 = 100(2^{8})$

[elfin schooner]

@burnt thorn

[burnt thorn]

btw, just want you to know that this is not where u messed up

[undone belfry]

A_8 equals 25600 though.

[burnt thorn]

it certainly does

and so what is half the capacity

[undone belfry]

12800

Ohhh I see where I messed up now!

[burnt thorn]

what is half of capacity not attendance

[burnt thorn]

👍

[undone belfry]

Half of the capacity is 31700.

[burnt thorn]

yep

so did the attendance pass half the capacity?

[undone belfry]

No

[burnt thorn]

✅

alr

[undone belfry]

So how do I find which hour then

Is the hour 8?

[burnt thorn]

since we know that the attendance is not yet at half the capacity, we have to increase the attendance. what variable can we manipulate to increase the attendance?

[undone belfry]

10 maybe 🤔

[burnt thorn]

we don't want to jump too much

1 at a time

so we should start with 9

,tex So if $n = 9$, solve for $A_n = 100(2^{n})$.

[elfin schooner]

@burnt thorn

[undone belfry]

51200

25600 is half of that

[burnt thorn]

yep

[burnt thorn]

completely irrelevant

so did the attendance pass the capacity

[undone belfry]

No

Because 63,400 is still bigger

[burnt thorn]

so?

||sry if i sound harsh||

[undone belfry]

So then it means it didn’t pass maximum capacity

Oh shoot

[burnt thorn]

lol

[undone belfry]

31700

[burnt thorn]

yep, thats half of the capacity

so did the attendance pass half the capacity

[undone belfry]

And it passed it

Yes

[burnt thorn]

✅

so 9 is your answer

on the 9th hour, the attendance was more than half the capacity

[undone belfry]

So if I were to organize the work I just did all nice and neat to summarize it up, what would I write.

[burnt thorn]

$\frac{63,400}{2} = 100(2^{n})$

[elfin schooner]

@burnt thorn

[burnt thorn]

,tex $317 = 2^{n}$

[elfin schooner]

@burnt thorn

[burnt thorn]

wait @undone belfry have you used log and ln

[undone belfry]

Logarithms? No, we haven’t.

[burnt thorn]

oh

then its gonna be a pain to right out everything

but its fine

[undone belfry]

I was supposed to do this without logarithms. Sorry about that

[burnt thorn]

so write smth like

[undone belfry]

Do I write what you previously put above or no?

[burnt thorn]

one sec i gotta hand write it

[undone belfry]

No worries. Once again, thank you so much four your time and help.

[burnt thorn]

@undone belfry there are 3 elements to the thing in the red circle

Do you know what each of them are?

[undone belfry]

We’re not working with any of that stuff though. My teacher wouldn’t want me even writing it.

[burnt thorn]

Oh then youre gonna have an even harder time

Cause now you gotta write English

“2^1 = 2, 2 is not more than 316”

[undone belfry]

My teacher wants it just in Arithmetic or Geometric Sequences.

[burnt thorn]

Bro this is so annoying

[undone belfry]

Is that not what we were doing?

[burnt thorn]

Ya but there are a bunch of easier ways to write this than just arithmetic/geometric sequences

So just say

[undone belfry]

I know I know. It is a pain, you’re right.

[burnt thorn]

,tex $2^{8} = 256$, $2^{9} = 512$

[elfin schooner]

@burnt thorn

[burnt thorn]

And just write ❌ next to the first equation and ✅ next to the second

K i gtg bye