[gmichnikov]

The upper age limit is 2t-14 (as you note earlier in your comment) rather than the 2t+14 you mention later.

Integrating, you get -20(e^(-0.05(2x-14)) - e^(-0.05(x/2+7)))

The derivative (eliminating the constant) is: (e^0.7)(-0.1)(e^(-0.1x))+(e^-0.35)(0.025)(e^(-0.025x))

Wolfram gives about 32.5 as the root. You can plot the integral (try www.coolmath.com/graphit) and mouse over to confirm.