Bacteria Growth

HeidiS

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Apr 28, 2006
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Word problem: The number of bacteria N in a culture is given by the model N = 250e^kt, where t is the time (in hours), with t= 0 corresponding to the time when N = 250. When t = 10, there are 280 bacteria. How long does it take the bacteria population to double in size? To triple in size?

I just don't get it! I think the e^k is hanging me up. Will you please help me get started? :?
 
You are given a known data point, (t, N) = (10, 280). Plug this information into the equation, and solve for the value of the growth constant "k".

Rewrite the equation, now complete with a value for "k". You are asked for the time "t" when N will equal 2(250) = 500. So plug "500" in for "N", and solve for the time "t". The same process applies for the "tripling" time.

If you get stuck, please reply showing how far you have gotten. Thank you.

Eliz.
 
I got 3 for k. Is this correct? The answer I got was 83.33 hrs to double and 166.67 to triple. Am I way off base, or did I get it right?
 
HeidiS said:
I got 3 for k. Is this correct?
Check it:

. . . . .t = 10:

. . . . .N = 250 e<sup>30</sup> = 2671618645000000

...approximately. (The number is too large for my calculator to report completely.) Since N was supposed to be only 280, not 2700 trillion, then "k = 3" is unlikely to be correct.

Please reply showing how you obtained this value, so we can try to find the error. Thank you.

Eliz.
 
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