**Question:**

The count of bacteria in a culture grows by 10% in the first hour, decreases by 8% in the second hour and again increases by 12% in the third hour. If the count of bacteria in the sample is 13125000, what will be the count of bacteria after 3 hours?

**Solution:**

Given:

$\mathrm{R}_{1}=10 \%$

$\mathrm{R}_{2}=-8 \%$

$\mathrm{R}_{3}=12 \%$

$\mathrm{P}=$ Original count of bacteria $=13,125,000$

We know that:

$\mathrm{P}\left(1+\frac{\mathrm{R}_{1}}{100}\right)\left(1-\frac{\mathrm{R}_{2}}{100}\right)\left(1+\frac{\mathrm{R}_{3}}{100}\right)$

$\therefore$ Bacteria count after three hours $=13,125,000\left(1+\frac{10}{100}\right)\left(1-\frac{8}{100}\right)\left(1+\frac{12}{100}\right)$

$=13,125,000(1.10)(0.92)(1.12)$

$=14,876,400$

Thus, the bacteria count after three hours will be $14,876,400$.