Question

The number N of bacteria in a culture is given by the model N=250e^kt where t is the time (in hours). If N=280 when t=10 estimate the time for the population to double in size.

Answer 1

First determine k from the information provided.

280 = 250*e^10k
ln(28/25) = 10 k
k = 0.01133 hr^-1

Now solve this equation for t:

500 = 250e^0.01133t
ln2 = .01133 t
t = 61.2 hours