Final answer:
To find out after how many minutes a swimming pool would overflow if water doubles every minute, we apply the exponential growth formula. Given an Olympic-size swimming pool with a volume of 2,500,000,000 mL, it would take approximately 36 minutes to overflow, thus the correct answer is B. 36.
Step-by-step explanation:
The question asks us to determine after how many minutes an Olympic-size swimming pool would overflow if we start with a drop of water (0.05 mL) and double the amount of water each minute. To find the answer, we need to understand the concept of exponential growth. An Olympic-size swimming pool has a volume of about 2,500,000 L, which is equivalent to 2,500,000,000 mL. We would start by converting the initial volume of the drop of water into the same unit for consistency, which gives us 0.05 mL.
Next, we apply the concept of exponential growth, where the amount of water doubles every minute. This is described by the formula V = V0 * 2t, where V0 is the initial volume, V is the final volume, and t is the time in minutes. To find the time it would take for the pool to overflow, we set V equal to the volume of the pool (2,500,000,000 mL) and solve for t.
Using the formula and solving for t gives us:
- 2,500,000,000 = 0.05 * 2t
- 50,000,000,000 = 2t
- t = log2(50,000,000,000)
- t ≈ 35.49
Since you can't have a fraction of a minute in this context, and the pool overflows after the minute mark is reached, you would need 36 minutes for the pool to overflow. Therefore, the correct answer is option B. 36.