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GOODMAN
 3 years ago
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.
GOODMAN
 3 years ago
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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GOODMAN
 3 years ago
Best ResponseYou've already chosen the best response.1Correct. Dont know where to start on this problem.

Libniz
 3 years ago
Best ResponseYou've already chosen the best response.1so in beginning there was 400

Libniz
 3 years ago
Best ResponseYou've already chosen the best response.1t represent time , what time do you see there

GOODMAN
 3 years ago
Best ResponseYou've already chosen the best response.1k. so the equation is \[5000=400e ^{k(1.25)}\]

GOODMAN
 3 years ago
Best ResponseYou've already chosen the best response.1Hmm...take ln of both sides and bring exponent down then solve for k?

GOODMAN
 3 years ago
Best ResponseYou've already chosen the best response.1\[\ln(5000)=k(1.25)\ln400e\]

GOODMAN
 3 years ago
Best ResponseYou've already chosen the best response.1How would you set it up?

Libniz
 3 years ago
Best ResponseYou've already chosen the best response.1I would divide both sides by 400 first

Libniz
 3 years ago
Best ResponseYou've already chosen the best response.1\[5000/400=e ^{k(1.25)}\]

Libniz
 3 years ago
Best ResponseYou've already chosen the best response.1now take ln of both sides

GOODMAN
 3 years ago
Best ResponseYou've already chosen the best response.1\[\ln(25/2)=k(1.25)lne\]

GOODMAN
 3 years ago
Best ResponseYou've already chosen the best response.1Wouldnt ln and e cancel eachother out though?

GOODMAN
 3 years ago
Best ResponseYou've already chosen the best response.1So basically, to get k, you would divide ln(25/2) by 1.25?

GOODMAN
 3 years ago
Best ResponseYou've already chosen the best response.1lol thanks. so to rewrite the equation, i would just plug everything in?

GOODMAN
 3 years ago
Best ResponseYou've already chosen the best response.1\[5000=400e ^{2.02(1.25)}\]

Libniz
 3 years ago
Best ResponseYou've already chosen the best response.1close but to be more general you use t instead of specific time

GOODMAN
 3 years ago
Best ResponseYou've already chosen the best response.1Ohh okay. So intead of 1.25, just t?

Libniz
 3 years ago
Best ResponseYou've already chosen the best response.1that way you can find y for any t value you plug in

GOODMAN
 3 years ago
Best ResponseYou've already chosen the best response.1So on b, you would plug n as 5000 and y as 1500?

Libniz
 3 years ago
Best ResponseYou've already chosen the best response.1exactly , this time you are finding the 't'

GOODMAN
 3 years ago
Best ResponseYou've already chosen the best response.1Because you divide by 5000 on both sides. Getting: \[\ln(3)=(2.02)\ln(e)\]

GOODMAN
 3 years ago
Best ResponseYou've already chosen the best response.1And then divide by ln(2.02) Did I do it right?

GOODMAN
 3 years ago
Best ResponseYou've already chosen the best response.1Thank God. lol. But would that be like 5 mins?

Libniz
 3 years ago
Best ResponseYou've already chosen the best response.1it will take .5438 hours

GOODMAN
 3 years ago
Best ResponseYou've already chosen the best response.1Nice to meet you too. It was good working with you.
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