Posted by **toma** on Tuesday, December 11, 2012 at 4:18am.

A bacteria culture contains 200 cells initially and grows at a rate proportional to its size. After half an hour the population has increased to 360 cells.

(a) Find the number of bacteria after t hours.

(b) Find the number of bacteria after 4 hours.

I found part a, P(t)= 200e^(1.2*t)

but when I solve part b it's different than the model answer!

- Calculus -
**Reiny**, Tuesday, December 11, 2012 at 7:44am
I found the following:

360 = 200 e^(.5k) , where k is a constant

1.8 = e^(.5k)

ln 1.8 = .5k lne

.5k = ln 1.8

k = 1.1755733..

so Number = 200 e^(1.755733t)

when t=4

number = 200 e^4.702293..

= 22039.9

or appr 22040 bacteria

It looks like you rounded of the value of k too early.

Since you are using a calculator anyway, why round off any numbers at all ?

Just use them the way they appear on your device, so there is no need to re-enter any numbers.

I also use the memory locations of my calculators to store any intermediate results.

If we use your value of k = 1.2

Number = 200 e^(4*1.2) = appr 24302 which is significantly different from the answer I got.

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