Assume that the number of bacteria follows an exponential growth model: . The count in the bacteria culture was 100 after 10 minutes and 1200 after 30 minutes. What was the initial size of the culture?

Question

3084 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-17T14:55:49

#"Approx. "29#.

Let, #N# denote the no. of bacteria after #t# minutes.

Given that, #N# follows an exponential growth model, we get,

# N=kb^t............(k,b" const.)"......(star)#.

To determine the consts. #k and b#, let us utilise the conds. :

#(i) : t=10, N=100, and, (ii) : t=30, N=1200#.

#(star), and (i) rArr 100=kb^10..........(star1)#, and,

#(star), and (ii) rArr 1200=kb^30..........(star2)#.

#:. (star2) -: (star1) rArr 12=b^20 rArr b=12^(1/20)#.

#"Then, by "(star1), k=100/b^10=100/(12^(1/20))^10, or, #

# k=100/12^(1/2)=100/sqrt(4xx3)=50/sqrt3=1/3*50sqrt3#.

With these #k and b#, we have,

#N=1/3*50sqrt3*12^(t/20)#.

To, get the initial size of the culture, we plug in #t=0#, & get,

#N=1/3*50sqrt3~~1/3(50)(1.7321)~~28.87=29#.