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Mathematics 23 Online
OpenStudy (anonymous):

Please help will fan and medal!!! Question attached in comments!!

OpenStudy (anonymous):

I think it's 2,520 @Susanna

OpenStudy (susanna):

I don't know this one, sorry...

OpenStudy (caozeyuan):

Well, it says t=o and P=1000, so what is A?

OpenStudy (susanna):

oops, I've got to go...

OpenStudy (boldjon):

i know it

OpenStudy (boldjon):

For bacterial growth you usually model them with an exponential formula: p(t) = p₀ e^(kt) p(t) : population at time t (1200) p₀ : initial population (1000) k : growth constant t : time in hours (2) Plug in what you know and solve for k: 1200 = 1000 e^(2k) Divide both sides by 1000: 1.2 = e^(2k) Take the natural log of both sides to cancel e on the right: ln(1.2) = 2k Divide both sides by 2: k = ln(1.2) / 2 k ≈ 0.0911607784 So your completed formula is: p(t) = 1000 * e^(0.0911607784t) To figure the population after 13 hours, just plug in t = 13: p(13) = 1000 * e^(0.0911607784 * 13) p(13) ≈ 3271

OpenStudy (anonymous):

Wait what is e? @boldjon

OpenStudy (boldjon):

oh i messed up i did 13 hours instead of 11

OpenStudy (boldjon):

hold up

OpenStudy (boldjon):

P(t) = 1000 * (1.2)^(t/5) {after 5 hours, it grows by a factor of 1.2} P(11) = 1000 * (1.2)^(11/5) ~= 1493 bacteria

OpenStudy (boldjon):

1493

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