The cost of controlling emissions at a firm goes up rapidly as the amount of emissions reduced goes up. Here is a possible model:
$C ( q ) = 4,500 + 200 q ^ { 2 }$
Where q is the reduction in emissions (in pounds of pollutant per day) and C is the daily cost (in dollars) of this reduction. If a firm is currently reducing its emissions by 12 pounds each day, what is the marginal cost of reducing emissions even further

A)$3,600
B) $4,800
C) $9,300
D) $1,200
E) $2,400

Question

The cost of controlling emissions at a firm goes up rapidly as the amount of emissions reduced goes up. Here is a possible model: 
 $C ( q ) = 4,500 + 200 q ^ { 2 }$ 
Where q is the reduction in emissions (in pounds of pollutant per day) and C is the daily cost (in dollars) of this reduction. If a firm is currently reducing its emissions by 12 pounds each day, what is the marginal cost of reducing emissions even further 
 
A)$3,600
B) $4,800
C) $9,300
D) $1,200
E) $2,400

Quizplus · Accepted Answer

The marginal cost of reducing emissions further is found by taking the derivative of the cost function $C(q) = 4,500 + 200q^2$ with respect to $q$, which gives $C'(q) = 400q$. Substituting $q = 12$ into this derivative gives $C'(12) = 400(12) = 4,800$.

The Cost of Controlling Emissions at a Firm Goes Up C(q)=4,500+200q2C ( q ) = 4,500 + 200 q ^ { 2 }C(q)=4,500+200q2

The Cost of Controlling Emissions at a Firm Goes Up $C ( q ) = 4,500 + 200 q ^ { 2 }$