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# Ex.8.3 Q11 Comparing Quantities Solutions - NCERT Maths Class 8

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## Question

In a Laboratory, the count of bacteria in a certain experiment was increasing at the rate of $$2.5\%$$ per hour. Find the bacteria at the end of $$2$$ hours if the count was initially $$\rm{}\,5, 06,000$$.

Video Solution
Comparing Quantities
Ex 8.3 | Question 11

## Text Solution

What is known?

Original Count, Time Period and Rate of Increase

What is unknown?

The total count after $$2$$ hours

Reasoning:

$$A = P \left( 1 + \frac{r}{100} \right)^{\rm{n}}$$

$$P= \rm{}\,5,06,000$$

$$N = 2$$ hours

$$R= 2.5\%$$ hour =\begin{align}\frac{{25}}{{10}} \end{align}hours

Steps:

\begin{align}A &= P\left( {{1 + }\frac{{r}}{{{100}}}} \right)^{n} \\ &= 506000\left( {{1 + }\frac{{{25}}}{{{1000}}}} \right)^{2} \\ &= 506000\left( {{1 + }\frac{{1}}{{{40}}}} \right)^{2} \\ &= 506000\left( {\frac{{41}}{{40}}} \right)^2 \\ &= 506000 \times \frac{{41}}{{40}} \times \frac{{41}}{{40}} \\ &= 506000 \times \frac{{1681}}{{1600}} \\ &= {506000} \times 1.050625 \\ &= 531616 \\ \end{align}

The total count of bacteria after $$2$$ hours $$=\rm{}\, 531616$$

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