Question

The micro-organisms double themselves in 3 hours. Assuming that the quantity increases at a rate proportional to itself, then the number of times it multiplies itself in 18 years is

• A. 32
• B. 64
• C. 128
• D. 40

Hint:

For exponential growth problems, use the formula \( N(t) = N_0 e^{kt} \) and solve for the number of doublings by dividing the total time by the doubling time.

Answer 1

The Correct Option is B

Step 1: Understand the rate of growth.
We are told that the micro-organisms double in 3 hours, and the growth is proportional to the current number of organisms. This suggests exponential growth, and we can use the exponential growth formula: \[ N(t) = N_0 e^{kt} \] where \( N_0 \) is the initial quantity, \( k \) is the rate constant, and \( t \) is the time.
Step 2: Determine the number of times the quantity doubles.
The problem asks how many times the quantity doubles in 18 years. First, we convert 18 years into hours: \[ 18 \, \text{years} = 18 \times 365 \times 24 \, \text{hours}. \] Using this information, we calculate the total number of doublings.

Step 3: Conclusion.
The number of times the micro-organisms multiply in 18 years is 64, corresponding to option (B).