Hotel Occupancy Rate The occupancy rate of the all-suite Wonderland Hotel, located near an amusement park, is given by the function r(t)-t3t2+t+60 (OStSIZ) s1 3 9 where t is measured in months, with t = 0 corresponding to the beginning of January. Management has estimated that the monthly revenue (in thousands of dollars/month) is approximated by the function R(r) = ;,3+i:2 (0: rs 100) 5000 so where r is the occupancy rate. (a) Find an expression r'(t) that gives the rate of change of Wonderland's occupancy rate with respect to time t. &,2_ EH m J "m = 81 3 9 (b) Find an expression R'(r) that gives the rate of change of Wonderland's monthly revenue with respect to the occupancy rate r. . __9_2 Q R")' 5000r+50r / (c) What is the rate of change (in dollars per month) of Wonderland's monthly revenue with respect to time at the beginning of January? At the beginning of July? (Hint: Use the chain rule to nd R'(r(0))r'(0) and R'(r(6))r'(6).) (Round your answers to the nearest integer.) January $ x permonth July :1; x per month