To preserve the ecological balance of a reserve, a number of lions were released in the reserve in 2000. Initially, there were only 5 lions in the reserve. After the observation of a few years, a function L(n)=(n+1)2+(n+1)+15 was developed to represent the number of lions in the reserve, where L(n) represents the number of lions and n represents the number of years after which they were released. Assume that no lion died during this period. Based on the above function, which of the following statements are correct? (without calculator) I- 10 lions were released in the reserve in 2000. II- The increase in the number of lions in the third year was 8. III- The total number of lions in the beginning of the third year was 27. A Only I B I and II C II and III D All three

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To preserve the ecological balance of a reserve, a number of lions were released in the reserve in 2000. Initially, there were only 5 lions in the reserve. After the observation of a few years, a function L(n)=(n+1)2+(n+1)+15  was developed to represent the number of lions in the reserve, where L(n) represents the number of lions and n  represents the number of years after which they were released. Assume that no lion died during this period. Based on the above function, which of the following statements are correct? (without calculator)  I- 10 lions were released in the reserve in 2000. II- The increase in the number of lions in the third year was 8. III- The total number of lions in the beginning of the third year was 27. A	Only I B	I and II C	II and III D	All three

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Initial Lion Count: Let's analyze the given function L(n) = (n+1)^2 + (n+1) + 15 to determine the correctness of the statements. First, we will check statement I: ＂10 lions were released in the reserve in 2000.＂ Since the function represents the number of lions after n years, we can plug in n = 0 for the year 2000 to find the initial number of lions. L(0) = (0+1)^2 + (0+1) + 15 L(0) = 1 + 1 + 15 L(0) = 17 This means there were 17 lions in the reserve in the year 2000, not 5 as initially stated or 10 as claimed in statement I.Increase Calculation: Next, we will check statement II: ＂The increase in the number of lions in the third year was 8.＂ To find the increase in the third year, we need to calculate the number of lions in the second year (n=1) and the third year (n=2) and then find the difference. L(1) = (1+1)^2 + (1+1) + 15 L(1) = 4 + 2 + 15 L(1) = 21 L(2) = (2+1)^2 + (2+1) + 15 L(2) = 9 + 3 + 15 L(2) = 27 The increase from the second year to the third year is L(2) - L(1) = 27 - 21 = 6, not 8 as claimed in statement II.Total Lions in Third Year: Finally, we will check statement III: ＂The total number of lions in the beginning of the third year was 27.＂ We have already calculated L(2) in the previous step, which is the number of lions at the beginning of the third year, and found it to be 27. Therefore, statement III is correct.

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