Calculus
posted by Oj .
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?

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 
Bacteria experiment. If after one hour there were 1600 bacteria. Three hours later there was 400 bacteria. How many bacteria were there originally?