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student
so sorry here.
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volunteer
Um, little bit lower.
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student
Right here.
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volunteer
Yeah
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student
All right
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student
I do, oh.
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student
OK. So, 1234 saving.
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student
So I go 3 and they go up 7.
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student
Look
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volunteer
Yeah, and you go up 7, but remember to do it from Y equals -1, not from when Y equals 0 on because you, you see the blue line? Like, that's where the reflection is over. So you start from that line when you count.
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student
Oh, OK, I appreciate.
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volunteer
Mm. Just, yeah, keep that in mind.
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student
Why, 2, sorry.
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volunteer
Mm
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volunteer
Yeah
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student
I'm a little songs. All righty. Mm.
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student
I'm going to one.
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student
Uh
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student
so it can be 6
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volunteer
Yes.
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student
Um, so.
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student
It's right here
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volunteer
Mm
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volunteer
Yeah
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student
Appreciate it. 2345, let's see.
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student
So here for this for last night.
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volunteer
Wait, hold on, let
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volunteer
me verify
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student
Yeah
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volunteer
Wait a minute. Oh, yeah, yeah, that's right.
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student
All right, so I do a thing with mouth real quick. But I think I understand it now too.
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student
So appreciate it too.
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volunteer
Um
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volunteer
I'm happy to help
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volunteer
Oh, you too. Thank you.
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volunteer
Bye.
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student
hi
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volunteer
hello!
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volunteer
What do you need help with today?
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student
I need help with this question
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volunteer
Okay! Give me a minute to read the question
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student
ok
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volunteer
I can't see the full question. Could you move the screen a little to the right?
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volunteer
thank you!
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volunteer
First, do you know the formula for continuous exponential decay?
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student
Yes
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volunteer
In the formula, you will plug a as the initial population which is a
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volunteer
and t = time taken which is 12 minutes
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volunteer
question a is just asking you to write the formula
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volunteer
For question b, you need to find r
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student
ok
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student
53
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volunteer
Did you get 53 for r?
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student
yes
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volunteer
r is not 53.
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volunteer
First you have to plug in your numbers in the formula, a=400, y=140, t=12 minutes in the formula y=ae^rt
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volunteer
did you plug in your values?
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student
yes
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volunteer
can you show me your equation?
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volunteer
Do you need help building your equation Maya?
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[ { "pii_type": "PERSON", "surrogate": "Maya", "start": 40, "end": 44 } ]
student
yes
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volunteer
Okay. For y, we will substitute the value 140. Can you write y equal 140?
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volunteer
We do the same with a =400, and t = 12. Don't focus on question b yet. We are trying to find r
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volunteer
Great job Maya! That's the first step
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[ { "pii_type": "PERSON", "surrogate": "Maya", "start": 10, "end": 14 } ]
volunteer
The next step is to divide both sides by 400. Can you do that for me?
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volunteer
Great! So what will our equation look like now?
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volunteer
Let's write it on the graph
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volunteer
So we can have more space!
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volunteer
This is what our equation looks like now. Can you see it on your screen Maya?
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[ { "pii_type": "PERSON", "surrogate": "Maya", "start": 72, "end": 76 } ]
student
yes
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volunteer
good! You can reqrite 140/400 as 7/20
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volunteer
rewrite*
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volunteer
Now we take the natural log on both sides.
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volunteer
Did you do that Maya?
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[ { "pii_type": "PERSON", "surrogate": "Maya", "start": 16, "end": 20 } ]
student
yes
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volunteer
So do you know what the equation will look like now?
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student
no
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volunteer
That's totally fine!
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volunteer
Once we take the natural log on both sides the equation will look like this
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volunteer
Did you get that?
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student
yes
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volunteer
What would you do next?
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volunteer
If you are not sure that is fine! Just let me know
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student
not sure
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volunteer
Thats okay!
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volunteer
Since we are finding r, we need r by itself.
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volunteer
So we divide both sides by 12 to get r by itself
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volunteer
We found r! Great job!
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volunteer
So now we have all the values we need for question b
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volunteer
we need a=400 and r=(ln(7/20))/12
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volunteer
Question be asks us how many bacteria there are 23 minutes after the beginning of the study. So we would substitute t with 23.
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volunteer
Do you know how to write the equation?
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student
no
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volunteer
thats okay.
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volunteer
I will write the new equation in pink.
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student
ok
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volunteer
this is what our new equation will look like
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volunteer
then we simplify our esponent
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volunteer
exponent*
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volunteer
You can rewrite this as
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