Question

The rate of increase of the population of bateria in a culture is proportional to the number of bacteria at any given instant. Assume the initial count of bacteria is 1000 and after 1 hour the amount is 1200. Find (i) the number of bacteria present immediately after 5 hours. (iii) the time lapse before the number reaches 4000

Answer 1

$f(t)=f_0e^{kt}$

$f_0=1000$

t=1 hour=60 min

$1200=1000e^{60k}$

$k=(ln(1200/1000))/60=0.003$

1. t=5hours=300 min

$f(300)=1000e^{0.003x300}=2489$

2.$4000=1000e^{0.003t}$

$t=(ln(4000/1000))/0.003=462 min$