Question:
The rate of growth of bacteria is proportional to the bacteria present. If it is found that the number doubles in 3 hours, then the number of times the bacteria are increased in 6 hours is
The rate of growth of bacteria is proportional to the bacteria present. If it is found that the number doubles in 3 hours, then the number of times the bacteria are increased in 6 hours is
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In exponential growth problems, if a quantity doubles in a fixed time, it will double repeatedly in equal time intervals.
Updated On: Mar 28, 2026
- 6 times the original
- 4 times the original
- 8 times the original
- 5 times the original
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The Correct Option is B
Solution and Explanation
Step 1: Understand the nature of growth.
Since the rate of growth of bacteria is proportional to the amount present, the growth follows the law of exponential growth.
Step 2: Use the given information.
It is given that the number of bacteria doubles in 3 hours. This means: \[ N(3) = 2N_0 \]
Step 3: Find growth in 6 hours.
Since 6 hours is twice 3 hours, the bacteria will double again in the next 3 hours. Hence: \[ N(6) = 2 \times 2N_0 = 4N_0 \]
Step 4: Final conclusion.
The number of bacteria after 6 hours becomes four times the original number.
Since the rate of growth of bacteria is proportional to the amount present, the growth follows the law of exponential growth.
Step 2: Use the given information.
It is given that the number of bacteria doubles in 3 hours. This means: \[ N(3) = 2N_0 \]
Step 3: Find growth in 6 hours.
Since 6 hours is twice 3 hours, the bacteria will double again in the next 3 hours. Hence: \[ N(6) = 2 \times 2N_0 = 4N_0 \]
Step 4: Final conclusion.
The number of bacteria after 6 hours becomes four times the original number.
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