Me number of mosquitoes in a field after a major rainfall is modeled by the function M defined by M(t) = -t³ + 12t² + 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. want to not enoason ovi.noithoito mion a sedlo do or doin to c.) For what values of t is the rate of change of the number of mosquitoes in the field increasing? Javistni oris no" bas 'g to toivaded odt sdirdeab or wolod side odini eshins gnizaim od ni liri (5) erowans Toy tot asceno svi sviter to eviten steibril 20 E-= 0>x>8- svitizo 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 an expression for the rate of change of the number of bats in the field at time t = a.

The number of thousand mp3 players produced per month by a certain manufacturer t months after the start of the year 2004 can be described by the function f(t)=0.2t^2 + 3t + 3 As they sell more players, the company's profit increases both because they are selling more players and because economies of scale mean they can produce each player more cheaply. The manufacturer's total profit (in thousands of dollars) when x thousand mp3 players are made is given by the function g(x)=0.01x^2 +4x +20 We assume that the company sells all of the mp3 players that it produces. Calculate the rate at which the sales of mp3 players increases (in thousands of players per month) in terms of t.   Rate of increase :  .4t +3 thousand players per month. Calculate the rate at which the manufacturer's profit increases (in thousands of dollars per thousand mp3 players) in terms of x.   Rate of increase :  .02x +4 thousand dollars per thousand mp3 players. ?? Calculate the rate at which the manufacturer's…

Find the first and second differences of equation f(x) = 10 – (4 – x)^2. Is it a quadratic function?