Posted by **Oj** on Thursday, January 3, 2013 at 3:24pm.

A colony of bacteria is grown under ideal conditions in a laboratory so that the population increases exponentially with time. At the end of 2 hours, there are 4,800 bacteria. At the end of 4 hours, there are 19,00 bacteria. How many bacteria were present initially?

- Calculus -
**Steve**, Thursday, January 3, 2013 at 7:05pm
A = P*e^kt

4800 = P*e^2k

19000 = p*e^4k

Now, 4800/p = e^2k, so

19000 = p*(4800/p)^2

19000 = 4800^2/p

p = 4800^2/19000 = 1212

just for grins, what's k?

4800=1212*e^2k

e^2k = 3.958

2k = ln 3.958 = 1.376

k = 0.688

so, A(x) = 1212*e^.688t

- Calculus -
**Anonymous**, Friday, October 17, 2014 at 6:15pm
Bacteria experiment. If after one hour there were 1600 bacteria. Three hours later there was 400 bacteria. How many bacteria were there originally?

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