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.

## Answer this Question

## Related Questions

- Calculus (math) - A bacteria culture grows with constant relative growth rate. ...
- MATH :) - 3. In Biology, it is found that the bacteria in a certain culture ...
- precalculus - A bacteria culture initially contains 1500 bacteria and doubles ...
- math - A bacteria culture starts with 260 bacteria and grows at a rate ...
- maths --plse help me.. - A bacteria culture has an initial population of 600. ...
- calculus - 2. The rate of change in the number of bacteria in a culture is ...
- algebra - Two Questions: 1) A certain radioactive isotope has leaked into a ...
- Calculus - Suppose that a population of bacteria triples every hour and starts ...
- CALCULUS - a bacteria culture grows with a constant per capita growth rate. ...
- Math - I need some help. A biologist finds that the population of a certian type...