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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?
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Solution
\[Given: \]
\[ R_1 = 10 % \]
\[ R_2 = - 8 % \]
\[ R_3 = 12 % \]
P = Original count of bacteria = 13, 125, 000
We know that:
\[P\left( 1 + \frac{R_1}{100} \right)\left( 1 - \frac{R_2}{100} \right)\left( 1 + \frac{R_3}{100} \right)\]
∴ Bacteria count after three hours \[= 13, 125, 000\left( 1 + \frac{10}{100} \right)\left( 1 - \frac{8}{100} \right)\left( 1 + \frac{12}{100} \right)\]
\[ = 13, 125, 000\left( 1 . 10 \right)\left( 0 . 92 \right)\left( 1 . 12 \right)\]
\[ = 14, 876, 400\]
Thus, the bacteria count after three hours will be 14, 876, 400.
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