X has half life on 70.86 days, Y has half life of 77.27 days. On Jan 1 at 12:00 o'clock, 815g of X was created and 800g of Y was created at the same time. On which day and time will the mass of X be equal to Y.

Question

dumbcow · Answer

use the half life to get the decay function for each X,Y
$$f(t)= M e^{-kt}$$
where M is initial mass
set f(t) = M/2 for half life and solve for k
$$e^{-kt^*} = \frac{1}{2}$$
$$k = \frac{\ln 2}{t^*}$$
where t* is half life in days

dumbcow · Answer

subbing k back in
$$f(t) = M (2^{-t/t^*})$$

dumbcow · Answer

setting masses of X,Y equal you get
$$815 (2^{-t/70.86}) = 800 (2^{-t/77.27})$$

dumbcow · Answer

$$t = \frac{\ln (800/815)}{\ln 2}*\frac{1}{(\frac{1}{77.27} - \frac{1}{70.86})}$$