Question

In a laboratory, the count of bacteria in a certain experiment was increasing at the rate of 2.5% per hour. What is the approximate count of bacteria at the end of 2 hours if the count was initially 5,06,000?

• A. 531616

Answer 1

The correct option is A 531616
Here, initial count (P) = 5,06,000
Rate of increase (R) = 2.5%
Time (n) = 2 hours

After 2 hours, number of bacteria,
$=P{(1+\frac{R}{100})}^n$

$=506000{(1+\frac{2.5}{100})}^2$

$=506000{(1+\frac{25}{1000})}^2$

$=506000{(1+\frac{1}{40})}^2$

$=506000{\left(\frac{41}{40}\right)}^2$

$=506000\times \frac{41}{40}\times \frac{41}{40}$

$=5,31,616.25$

Approximate count of bacteria after 2 hours is 531616.