Predict a record time without rounding away the result

Plot year horizontally and $t$ vertically. The source defines $t$ as seconds above 210 seconds, not the total race time. The curve decreases and appears to flatten somewhat; all eight exact observations are retained. The second panel supplies the transformed plot used in (iv).

The scatter is decreasing with some flattening, while a straight line enforces a constant rate of improvement. In this context a record series need not continue improving at a constant rate indefinitely. Extrapolating a decreasing line far enough eventually predicts an impossible nonpositive total race time. Merely predicting a negative offset is not itself proof of impossibility: 3 min 30 s is a chosen baseline, not a demonstrated physical limit.

A nonconstant quadratic has unbounded eventual behaviour. An upward quadratic eventually turns upwards and predicts rising record times, contrary to using a retained best-time record in the same event; a downward quadratic eventually gives nonpositive total times. The finite historical data do not justify either long-term trend. This is an authored explanation of the source’s contextual ask, not an empirical prediction about later real records.

The full independently calculated fit is $\ln t=a+bx$, with retained coefficients

$\begin{aligned}a&=34.85307066132827,\\b&=-0.016127950773425652.\end{aligned}$

It agrees with the printed rounded form $\ln t=34.9-0.0161x$. For the prediction use the retained coefficients, not the rounded form: the large year causes substantial cancellation between intercept and product.

$\begin{aligned}&t_{2010}\\ & =e^{a+2010b}\\ & =11.4259788212\ldots.\end{aligned}$

Add the baseline 210 seconds: total 221.4259788212 seconds, or 3 min 41.4 s, matching the printed answer. Using the rounded equation gives a different result and is not justified for this calculation. The year 2010 is outside 1930–2000, so this is extrapolation; even a close transformed fit does not guarantee the record’s future development. The model’s asymptote at 210 seconds is an assumption of this offset-exponential form, not a proven physical minimum.