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

• A. 6 times the original
• B. 4 times the original
• C. 8 times the original
• D. 5 times the original

Hint:

In exponential growth problems, if a quantity doubles in a fixed time, it will double repeatedly in equal time intervals.

Answer 1

The Correct Option is B

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.