# 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

#### 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#