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?

1 Answer
Feb 17, 2018

"Approx. "29Approx. 29.

Explanation:

Let, NN denote the no. of bacteria after tt minutes.

Given that, NN 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.