Question

A bacterium divides every $35$ minutes. If a culture containing $105$ cells/mL is grown for $175$ minutes, what will be the cell concentration/mL after $175$ minutes?

• A. $5\times 10^5$ cells
• B. $35\times 10^5$ cells
• C. $32\times 10^{5}cells$
• D. $4.175\times 10^5$ cells

Answer 1

Answer: (C)

Total number of bacteria produced $=2^n$
$n=\frac{\text{ Total time }}{\text{ Time of division }}=\frac{175}{35}=5$
Thus, after $5$ divisions total number of bacteria will be $2^5=32$. Initially there are $10^5$ bacteria/mL and therefore, after $175$ minutes, the concentration of bacterial cells will be $32\times 10^5$ or $3.2\times 10^{6}cells/mL$.