3. A biologist measures the amount of contaminant in a lake four hours after a chemical spill and again 12 hours after the spill. She sets up two possible models to determine Q, the amount of chemical remaining in the lake as a function of t, the time in hours.
a. In the first model, she assumes that the contaminant is leaving the lake at a constant rate of 5 tons/hour and that the lake will be free of contaminant 30 hours after the spill. Based on this model, find a formula for Q(t), the quantity (in tons) of contaminant remaining in the lake as a function of time. What were the amounts measured at four and 12 hours?
b. In her second model, she assumes that the amount of contaminant decreases exponentially. Using the data available, find another formula for Q(t). Interpret what each of the parameters means in the context of this problem.
c. She measures the contaminant again 19 hours after the spill and finds that 65 tons remain. Based on this evidence, which model seems best? EXPLAIN.