- #1

KevinL

- 37

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Assume that bacteria in aculture grows according to an exponential growth model. If the number of bacteria grows from 50 to 1000 in 12 hours:

a)How many bacteria will be present after 18 hours?

b)How long does i take for the number of bacteria to double?

A) db/dt = kb, b(0) = 50

b(t)=ce^(kt)

b(0)=50=ce^(k*0)

c=50

b(12)=50e^(k*12) = 1000

e^(k*12)=20

k=12*ln(20)

k=35.94 >>>> .359

Now that I have c and k I can find how much bacteria there is at 18 hours. So:

b(18) = 50e^(.359*18) = 32017

B) I am assuming they mean double as in get to 2000 bacteria. So:

2000=50e^(.359*t)

40=e^(.359t)

ln(40)/.359 = t

10.2 = t

How can it be at 2000 at 10 hours when I already know that 2 hours later its only at 1000? I must have screwed something up.