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A bacteria culture will grow from 400 to 5000 in 1 1/4 hours. a) Find the constant k for this bacteria using growth formula, y=ne^kt, and write the growth equation. b)Use your equation to predict how much longer it will take the 5000 bacteria to become 15000 bacteria.

Mathematics
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\[y=ne^{kt}\]
n is beginning y is end
Correct. Dont know where to start on this problem.

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Other answers:

so in beginning there was 400
so plug in 400 for n
plug in what for y?
5000?
yes
\[5000=400 e^{kt}\]
t represent time , what time do you see there
t would go in as 1.5
1 1/4= 1.25
I knew that.
let's go with that
k. so the equation is \[5000=400e ^{k(1.25)}\]
yes
your job is to find k
Hmm...take ln of both sides and bring exponent down then solve for k?
exactly
\[\ln(5000)=k(1.25)\ln400e\]
not what I would do
How would you set it up?
I would divide both sides by 400 first
Ohh okay.
\[5000/400=e ^{k(1.25)}\]
now take ln of both sides
\[\ln(25/2)=k(1.25)lne\]
Wouldnt ln and e cancel eachother out though?
yes
So basically, to get k, you would divide ln(25/2) by 1.25?
yes
k=2.02?
yes
lol thanks. so to rewrite the equation, i would just plug everything in?
\[5000=400e ^{2.02(1.25)}\]
close but to be more general you use t instead of specific time
Ohh okay. So intead of 1.25, just t?
\[y=400e ^{2.02(t)}\]
that way you can find y for any t value you plug in
So on b, you would plug n as 5000 and y as 1500?
*15000
exactly , this time you are finding the 't'
I got 0.5438
Because you divide by 5000 on both sides. Getting: \[\ln(3)=(2.02)\ln(e)\]
And then divide by ln(2.02) Did I do it right?
yes
Thank God. lol. But would that be like 5 mins?
what?
.5438
yes ,
it will take .5438 hours
okie dokes.
Thanks youuuu!!
nice to meet you
Nice to meet you too. It was good working with you.

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