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**lemontea** The occupancy rate of the suite wonderland hotel located near an amusement park is given by the function

r(t)=10/81t^3 -10/3t^2+ 200/9t+60 (0<t<12)

where t is measured in months with t=0 corresponding to the beginning of January. Management has estimated that the montly revenue (in thousands of dollars/month) is approx by the function

R(r)=-3/5000r^3 + 9/50r^2 (0<r<100)

where r is the occupancy rate

a) Find an expression that gives the rate of change of Wonderland's occupancy rate with respect to time