Let $Q(t)$ represent the amount of a certain reactant present at time $t$. Suppose that the rate of decrease of $Q(t)$ is proportional to $Q^3(t)$. That is, $Q^{\,\prime} = -kQ^3$, where $k$ is a positive constant of proportionality.

1. Suppose $\displaystyle Q(0) = \frac{1}{2}$. How long will it take for the reactant to be reduced to one half of its original amount?
   
   $t =$ help (numbers)
   
   
2. Suppose $\displaystyle Q(0) = \frac{1}{4}$. How long will it take for the reactant to be reduced to one half of its original amount?
   
   $t =$ help (numbers)
   
   
3. Recall that, in problems of radioactive decay where the differential equation has the form $Q^{\,\prime} = -kQ$, the half-life was independent of the amount of the amount of radioactive material initially present. What happens in the case of $Q^{\,\prime} = -kQ^3$? Does half-life depend on $Q(0)$, the amount initially present?
   Choose yes no cannot be determined