Let m be the tumor mass, then

dm/dt = k t,

so:

m= k t^2/2 + m0,

where m0 is the initial mass.

The avarage mass in the interval t1 to t2 is:

integral_{t=t1 to t2) m(t) dt / (t2-t1) = [k t2^3/6 + m0 t2 - kt1^3/6 - m0 t1]/(t2-t1)

So now we want to put t1=26, t2=52, and find t such that:

m(t) = [k 52^3/6 + m0 52 - k 26^3/6 - m0 26]/26 = k(2 52^2 - 26^2)/6 + m0

So:

t^2 = (2 52^2 - 26^2)3

hence:

t ~= 39.7

RonL

(check the arithmetic and algebra please).