The number N of bacteria present in a culture at time t (in hours) obeys the fun
ID: 3089706 • Letter: T
Question
The number N of bacteria present in a culture at timet (in hours) obeys the function N(t) =1500e0.01t. (a) Determine the number of bacteria att = 0 hours.1
(b) What is the growth rate of the bacteria?
2%
(c) What is the population after 2hours?
3
(d) When will the number of bacteria reach 2300?
4 hours
(e) When will the number of bacteria double?
5 hours (a) Determine the number of bacteria att = 0 hours.
1
(b) What is the growth rate of the bacteria?
2%
(c) What is the population after 2hours?
3
(d) When will the number of bacteria reach 2300?
4 hours
(e) When will the number of bacteria double?
5 hours
Explanation / Answer
b: 0.01x100=1, so the growth rate is 1% c: plug 2 in for t. ==1530.3 d: set N(t)=2300. divide 2300 by 1500.take the ln of both sides to get ln2300/1500=lne^0.01t
this is equal to ln2300/1500=0.01t
divide both sides by 0.01
t=42.74hrs
e: do the same for N(t)=3000 t=69.31hrs