How do you find the size of the bacterial population after 100 minutes if a bacteria culture initially contains 1500 bacteria and doubles every half hour and the formula for the population is, #p (t) = 1500e^(kt)# for some constant, k ?
1 Answer
Explanation:
Given
#3000 = 1500 * e^(30k)#
That is
#2= e^(30k)# .
Take log on both sides to get
#30k = ln2 => k= ln2 /30#
Now
#p(100)= 1500 * e^(100k)#
#p(100)= 1500 * e^(10/3 ln2)#
#p(100)= 1500 * e^(ln(2^(10/3))#
#p(100)= 1500 * 2^(10/3)#
#p(100)= 1500 * 10.079 = 15119#
