A culture of bacteria obeys the law of uninhibited growth. If 500 bacteria are present -see below for question

A culture of bacteria obeys the law of uninhibited growth. If 500 bacteria are present initial¬ly and there are 800 after 1 hour, how many will be pre¬sent in the culture after 5 hours? How long is it until there are 20,000 bacteria?

A culture of bacteria obeys the law of uninhibited growth. If 500 bacteria are present -see below for question
Okay, letting n be hours, f be final and i be initial, then


f=ip^n with be p being percent growth.


So, 800=500p^1.


SO, 800/500=p.


So, f=500(8/5)^5 = 5242.88.





Now 20000=500(8/5)^n.


So, 40=(8/5)^n.


So, log40=n*log(8/5),


or log40/log(8/5)= n = 7.8486 hours approximately.