The occupancy rate of the all-suite Wonderland Hotel, located near an amusement park, is given by the function 10 r(t)= + 81 200 9 +60 (0 sts 12) 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 3 R(r) + 5000 9 50 (0 rs 100) 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. 10/2 r'(t)= 27 201 3 200 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. R'(r) = 9,2 5000 9r 25 (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 April? (Hint: Use the chain rule to find R'(r(0))r(0) and R (r(3))r'(3).) (Round your answers to the nearest integer.) January April $ per month: $ per month