A 10 kL tank of water provides water for a small village. Water is drunk from the tank at a rate of 1000 L per day, and the water is replenished at the same rate. Unfortunately, the filter/purifier for the intake water is malfunctioning. Conse quentially the water that is replenishing the tank is contaminated; it contains 0.00125 mg/L of heavy metals. Suppose that when the contamination was discovered the tank was 3/4 full and contained a, mg of heavy metals. Find a formula, A(t), for the amount of heavy metals in the tank at time t. Hint: make sure your units are consistent for all quantities. We suggest mg/kL If the concentration of heavy metals in the water is below 0.001 mg/L then the water is still safe to drink. You may assume that the heavy metals in the tank are well mixed (and thus evenly distributed) in the tank. The maintenance company has been notified, and have indicated that the they'll be on premises to service the filter/purifier in 7 days (and please make sure some- body is on premises during that entire day). However, we know from experience that they can be anywhere up to 3 days late. (ii) If the initial amount of heavy metals in the tank was 2 mg, will the concen- tration reach dangerous levels before the company services the tank? (Yes, no, or maybe?). Justify your answer. (iii) What is the largest initial amount of heavy metals that will definitely not reach dangerous levels before the company services the tank?