A chemical reactor contains a substance whose concentration (in mol/L) changes at a rate modeled by
r(t)=t2−6t+205,0≤t≤10,
where t is measured in hours.
(a) Determine the exact total change in concentration, in mol/L, that occurs between t=2 hours and t=10 hours.
(b) Show that r(t) is positive for all t in the interval [2,10]. Interpret the sign of r(t) in this context.
(c) The facility has a safety limit of a 0.50 mol/L increase in concentration over any eight-hour period. Based on your result in part (a), state whether the process remains within the safety limit over the interval [2,10]. Provide a clear justification.