In Exercises 1 and 2 assume that the populations grow expone

In Exercises 1 and 2, assume that the populations grow exponentially, that is, according to the law N(t) = N_0 e^kt. At the start of an experiment, 2000 bacteria are present in colony. Two hours later, the population is 3800. Determine the growth constant k. Determine the population live hours after the start of the experiment. When will the population reach 10,000?

Solution

N = No*e^kt

a) 3800 = 2000*e^(k*7200)

k = 8.915*10^-5

b) N = 2000*e^(8.915*10^-5*18000) = 9952.73

c) 10000 = 2000*e^( 8.915*10^-5*t)

t = 18053.15 sec = 5.015 hr