A mathematical model for the

rate at which a drug disseminates into the bloodstream

is given by

where r and k are positive constants. The function x$($t$)$

describes the concentration of the drug in the blood$-$

stream at time t$.$

$($a$)$ Since the DE is autonomous, use the phase portrait

concept of Section $2\mathrm{.}1$ to find the limiting value of

x$($t$)$ as t :

$.$