how resolve this problem Exponential Growth and Decay If y is a differentiable function of t such that y 0 and y ' = ky, for some constant k, then y = Cekt. C is the initial value of y, and k is the proportionality constant. Exponential growth occurs when k 0, and exponential decay when k

Question

how resolve this problem Exponential Growth and Decay
If y is a differentiable function of t such that y > 0 and y ' = ky, for some
constant k, then y = Cekt. C is the initial value of y, and k is the
proportionality constant. Exponential growth occurs when k > 0, and
exponential decay when k < 0.
Situation
10 grams of plutonium isotope Pu-239 is released in some far off nuclear
research facility. They have exposed the 10 grams of Pu-239 to air, so it has
turned yellow from its original silver like appearance. You're job is to find out
how long it will take for the 10 grams of Pu-239 to decay

anonymous · Answer

Shouldn't it take forever?  The plutonium should decay with half lives, so there should always be some left.  Looking at the equation $$ Ce^{kt}$$, if k is negative, then as t increases it will approach 0, but it will never be be perfectly 0.