Although a calculator is permitted, ALL WORK must be shown.

Please provide detailed answers to the questions listed below.

This Question is **CALCULATOR ACTIVE** A 16,000-liter swimming pool is filled to the rim. At time t= 0, water begins to drain out of the pool due to a leak. Water drains out of the pool at a rate modeled by R(t), measured in liters per hour, where R is given by the piecewise function 800t R(t) = t +4 950e'"5' fort > 6 forOStS6 (a) Is R continuous at t = 6? Show the work that leads to your answer. (b) Find the average rate at which water is draining from the pool between t=0 and t= 10 hours. (c) Find R'(4). Using correct units, explain the meaning of that value in the context of the problem. (d) Write, but do not solve, an equation involving an integral to find the time S when the amount of water in the pool is 12,000 liters