Question

The number of mosquitoes in a field after a major rainfall is modeled by the function M defined by M(t) = -t + 12t + 144t, where t is the number of days after the rainfall ended and 0 t 18.

(a) Using correct units, interpret the meaning of M' (15) = -171 in the context of the problem.

(b) Based on the model, what is the absolute maximum number of mosquitoes in the field over the time interval 0 t 18? Justify your answer.

(c) For what values of t is the rate of change of the number of mosquitoes in the field increasing?

(d) For 0 t 18, the number of bats in the field is modeled by the differentiable function B, where B is a function of the number of mosquitoes in the field. Based on the models, write the expression for the rate of change of the number of bats in the field at time t = a.