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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 $$5,06,000$$.


Solution

We have, $$P_0 $$ $$=$$ Original count of bacteria $$=506000$$,
Rate of increase $$=R =2.5\%$$ per hour,
Time $$=2$$ hours

$$\therefore$$ Bacteria count after $$2$$ hours $$=$$ $$P$$


$$P = P_0(1 +\dfrac{R}{100})^T$$


$$=506000\times {\left(1+\dfrac{2.5}{100}\right)}^{2}$$


$$=506000\times \dfrac{102.5}{100}\times \dfrac{102.5}{100}$$


$$=531616.25=531616$$ (approx)


Mathematics

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