Suppose()q(t) is a quantity that is varying over time according to rate function ()r(t), and it is modelled that()=()[+()].r(t)=q(t)[t+q(t)].

1. If there exists a solution function ()q(t) that satisfies (1)=2q(1)=2, what will be that quantity's rate of variation at =1t=1 ?
2. If a direction field for this rate equation were drawn, at what points in the tq-plane would the line segment drawn be horizontal?

REMINDER: not permitted to use any kind of technology,whether on- or off-line, to assist with any part of this calculation except simple arithmetic.