Question

A bacterium divides every $35$ minutes. If the culture containing ${10}^5$ $cells/ml$ is grown for $175$ minutes, what will be the concentration after that period?

• A. $175\times {10}^{5}cells/ml$
• B. $35\times {10}^{5}cells/ml$
• C. $5\times {10}^{5}cells/ml$
• D. $32\times {10}^{5}cells/ml$

Answer 1

Answer: (D)

$32\times {10}^{5}cells/ml$

In the given example, culture divides every 35 minutes. So in 175 minutes, it will divide 175/35 = 5 times.

Now, N${}_t$ = N${}_0$ x 2${}^n$

WhereN${}_t$ = final number of cells

N${}_0$ = initial number of cells

n = number of generation

If the culture initially contains 10${}^5$ cells/ml, the concentration after 175 minutes will be 10${}^5$ x 2 ${}^5$ = 32 x 10${}^5$ cells/ml.

Thus, the correct answer is option D.