Solution (source code)

= Solution

The change in inverse <temperature> is $\Delta u=1/290-1/300=1.14943\times10^{-4}\ \mathrm{K^{-1}}$. Treating the sensitivity as approximately constant over the interval,
$$
\Delta\ln[\mathrm O_3]\simeq1242\Delta u=0.142759,
\qquad
\boxed{\frac{[\mathrm O_3]_{290}}{[\mathrm O_3]_{300}}
\simeq e^{0.142759}=1.15345.}
$$
Thus the predicted <concentration> increases by \b[about 15.3%]. Linearizing the exponential gives a rougher 14.3% estimate; a logarithmic change is not itself the exact fractional change.

An independent finite-change calculation checks this approximation without keeping the loss ratio artificially fixed. Normalize the initial Chapman and nitrogen-cycle loss terms to 1 and 3, so the initial production is 4. If $r=X_{290}/X_{300}$, the new steady balance is $e^{-2610\Delta u}r^2+3e^{-1200\Delta u}r=4$. Its positive root is $r=1.15342$, essentially the same result.