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