The count of bacteria in a certain experiment was increasing at the rate of 2% per hour.

Initial count of bacteria, $P=500000$

Rate of increase, $R=2 \%$

Time, $n=2$ hours

Then the count of bacteria at the end of 2 hours is given by

Count of bacteria $=P \times\left(1+\frac{R}{100}\right)^{n}$

$=500000 \times\left(1+\frac{2}{100}\right)^{2}$

$=500000 \times\left(\frac{100+2}{100}\right)^{2}$

$=500000 \times\left(\frac{102}{100}\right)^{2}$

$=500000 \times\left(\frac{51}{50}\right)^{2}$

$=500000 \times\left(\frac{51}{50}\right) \times\left(\frac{51}{50}\right)$

$=(200 \times 51 \times 51)$

$=520200$

Therefore, the count of bacteria at the end of 2 hours is 520200 .