How long will it take plutonium-240 to decay 25% of it's original amount?

The weight of the plutonium isn't known, but we want to find how long it will take for the element to decay 25%. Let P = the original amount. The decay model is Q (t) = q0e^ (-rt). So q0 = P and we want a 1/4 of P. So Q (t) = (1/4) P

Since r = 0.00011, we have (1/4) P = Pe^ (-0.00011t).

Now divide both sides by P.

1/4 = e^ (-0.00011t)

Take the natural log of both sides:

ln (1/4) = - 0.00011t

Divide by - 0.00011

t = ln (1/4) / - 0.00011 = approx 12,602.676 years