Answer to Question #142509 in Differential Equations for danny

Question

the function q(t)=q.e^-kt may be used to model radioactive decay. Q represents the quantity remaining after t years; k is the decay constant. the decay constant for polutonium-240 is k+0.00011. what is the half life in year?

Answer 1

$\begin{aligned} q(t) &= qe^{-kt}\\ \\ \dfrac{q(t)}{q} &= e^{-kt}\\ \\ 0.5 &= e^{-kt}\\ (k = 0&.00011)\\ e&^{-0.00011t} = 0.5\\ -0.0001&1t = ln(0.5)\\ t &= \dfrac{ln(0.5)}{-0.00011}\\ \\ t &= \dfrac{-0.693}{-0.00011}\\ \\ \therefore t_{\frac{1}{2}} &= 6301.34 years \end{aligned}$

The half life in years is approximately 6301 years.