anonymous
  • anonymous
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
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\[y=ne^{kt}\]
anonymous
  • anonymous
n is beginning y is end
anonymous
  • anonymous
Correct. Dont know where to start on this problem.

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

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