I03-06

Official Solution:


Test one of the largest increases in the shortest period of time using the provided calculator. Nagahama beach had an initial estimate in 1997 of 106 nests and an estimate of 612 nests 17 years later for 2013. The total percent increase in that time was equal to (612 - 106) / 106 × 100 = 477%. That percentage divided by the 17 years would be approximately 34% per year.

Statement 1:

Based on the table, the prefectures that did not experience an increase in nest counts from past estimates to 2013 are:

• Tokushima (Hiwasa): Decreased from 76 to 18.

• Fukuoka (Shingu): Remained unchanged at 15.

Therefore, this statement is True.

Statement 2:

The greatest increase occurred at Nagahama Beach, where the nest count rose from 106 to 612, representing an increase of approximately six times, which corresponds to a 500% increase, not 600%. Therefore, this statement is False.

Statement 3:

From 1989 to 2013, the nest count at Maehama Beach increased from 611 to 1,637, corresponding to more than 2.5 times increase over 24 years: \(611*rate^{24} =1,637\). If the rate remains the same, in 12 years, the nest count becomes \(1,637*rate^{12}\). Since \(rate^{24} ≈ 2.5\), then \(rate^{12}=\sqrt{2.5}\). The square root of 2.5 is more than 1.5 (\(1.5^2 = 2.25\)), thus \(rate^{12} > 1.5\). This means that the nest count from 1,637 will increase by more than 50%, resulting in more than 2,400 nests in 2025.


Correct answer:

Based on the table, exactly two prefectures, based on their total nest counts, did not experience an increase from past estimates to 2013. "True"

Based on the table, the greatest percentage increase in nest counts from past estimates to 2013 was approximately 600%. "False"

If the annual percentage rate of increase at Maehama Beach remained constant from 1989 to 2013 and continues at the same rate until 2025, the estimated nest count in 2025 will exceed 2,400. "True"

I have revised the question, solution, and formatting by adding more details to enhance clarity.

Please read carefully. The statement talks about the prefectures, not beaches.

Based on the table, exactly two prefectures, based on their total nest counts, did not experience an increase from past estimates to 2013. "True"

Sorry, I don't understand why Aichi is not included in the counting of prefectures - it is clearly stated under Prefecture name and there are 3 prefectures not experiencing increase, can you help?

Thank you Bonuel, I got it!

Not sure how that reply got sent by me but I did want to mention that the answer to this question was a little confusing as it didn't mention the point about the prefecture Aichi having multiple beaches and adding that up would result in total count being greater

Here is the first statement:

Based on the table, exactly two prefectures, based on their total nest counts, did not experience an increase from past estimates to 2013.

The mention of "total nest count" for the prefectures should hint that there might be more than one beach in a prefecture. Additionally, this is a table-based question where you are expected to sort the data by different parameters and analyze it. After all, not everything will be handed to you on a platter, right?

I like the solution - it’s helpful.

I like the solution - it’s helpful. tricky, the first one

This is a great question that’s helpful for learning.

I don’t quite agree with the solution. In case of statement 3, Why is the rate not considered as (1637-611)/(2013-1989)? This was the value at 2025 does not exceed 2500.

Here is the third statement:



In statement 3, the solution uses compound growth because the counts grow by a percentage each year, not by a fixed number of nests per year.

Your method, using (1637 - 611) / (2013 - 1989), gives the average increase in the number of nests per year, not the average percentage growth per year. That is why it does not match the correct approach and leads to the wrong projection for 2025.