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Home » Now, apply the formula for the radius: - IQnection

Now, apply the formula for the radius: - IQnection

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 But $ t = 4.1 $ is in the year 2004 (since $ t = 0 $ is 2000). So the anomaly first exceeds 3.0 during 2004, but the official year is 2004. However, the first full year where its above is 2005? But the model is continuous. Typically, we report when it crosses.

📌 However, at $ t = 4 $, $ T = 3.0 $, so to exceed, $ t > 4 $. The next whole year is 2005, but the model is valid for all $ t $. The smallest year is $ 2000 + 4 = 2004 $, but since its equal at 2004, and increases, the first time it exceeds is in 2004? But exceed means $ > 3.0 $, so $ t > 4 $. Thus, the first full year is not yet 2005? But 2004 is $ t = 4 $.

📌 The temperature is 3.0 at $ t = 4 $, so the next instant it exceeds. Since 2004 is part of the continuous model, and the question asks for the year, we report 2004 only if it first exceeds during that year. But 2004 already reaches it. Does it exceed? No, it is equal. So the first year when it exceeds is 2005? But 2004.1 is in 2004.

📌 The answer should be the calendar year when it first happens: since $ t = 4 $ is 2004, and it crosses at 4, then in 2004 it exceeds (because $ t > 4 $ includes 2004.1), but 2004 is the year.

📌 Actually, $ t = 4 $ corresponds to the beginning of 2004. The temperature reaches 3.0 at the start of 2004, so it exceeds immediately. Thus, at some point in 2004, it exceeds. So the year is 2004.

📌 But to be precise: $ T(t) > 3.0 $ for $ t > 4 $. $ t = 4 $ gives $ T = 3.0 $, so $ t > 4 $ is required. Therefore, the first time is in 2004 (since $ t = 4 $ is boundary), but the event occurs during 2004. The question asks for the year, so we report 2004.

📌 But lets check $ t = 4.1 > 4 $: $ T = 3.045 > 3.0 $. So the event occurs at $ t = 4.1 $, which is in 2004.

📌 But earlier calculation: $ t = 4 $ gives $ T = 3.0 $, so the first time it exceeds is just after 2004. So the answer is 2004.

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