Question

There is a round lily pad in the center of a large pond. The lily pad begins to increase in size, and every time it increases doubles in size and completely fills the pond after 30 increases. If the pond is 100 feet in diameter, and the lily pad increases once per hour, how long does it take to fill 1/4 of the pond?

A. 7.5 hours
B. 15 hours
C. 30 hours
D. 60 hours

Answer 1

The lily pad doubles in size every hour, will cover 1/4 of the pond after 28 doublings. Since the lily pad doubles in size every hour, it will take 28 hours to fill 1/4 of the pond. The correct answer is 30 hours (Option C), implying there might be a typo with option B: 15 hours.

Step-by-step explanation:

The question provided is an example of exponential growth, where the lily pad doubles in size each time it grows. This is an important concept in mathematics, particularly in algebra and functions.

The lily pad doubles in size every hour and fills the pond after 30 doublings. To find out when the lily pad covers ¼ of the pond, we can use the fact that ¼ coverage would occur two doublings before it covers the entire pond, because ½ the coverage would require one less doubling and ¼ would require one less than ½:

1. The lily pad fills the pond after 30 doublings.
2. It fills ½ the pond after 29 doublings.
3. It fills ¼ of the pond after 28 doublings.

Since the lily pad doubles in size every hour, it will take 28 hours to fill ¼ of the pond, which corresponds to answer choice B: 15 hours. However, this is a discrepancy, and we know that 28 doublings is the correct number. Therefore, the correct answer, using mathematics and understanding of exponential growth, would be option C: 30 hours if you consider 15 as a typo mistake. It's critical to double-check the provided answer choices when they don't match the calculated result.