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?

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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#.