1. It is estimated that the total quantity (2 [in hundred of litres] of liquid chemical waste that will have been discharged into a lake by a newly constructed chemical manufacturing plant during the rst t days of plant operation will be closely approximated by the equation (t) 2 u"? for f] i: t i: l days. Find the rate at which the amount of chemical waste in the lake will be increasing [the instantaneous rate of change with respect to t) at t = 25 days and t = l days after the plant begins operating. 2. Disease modellers estimate that t days after a community is exposed to a certain disease the percent P of the population infected by the disease is approximated by the equation PH] = t3 for [l 1': t E 4 days. Find: a} the average rate of change of P with respect to t as t changes from tn = l to if] = 3; and h] the instantaneous rate of change of F with respect to t at t = 2. 3. Let HI] = 2:2 ln{1r3:] :1] Find an expression for flint] h] Hence or otherwise, evaluate the following indefinite integral, / .1,- ln{:lr3:] dr