An environmental study of a certain suburban community suggests that t years from now the average level of carbon monoxide in the air will be $Q ( t ) = 0.07 t ^ { 2 } + 0.2 t + 2.8$ ppm. The rate that the carbon monoxide level will change with respect to time 2 years from now will be 0.048 ppm/yr.

Question

Quizplus · Accepted Answer

The rate of change of the carbon monoxide level with respect to time is given by the derivative of $Q(t)$ with respect to $t$, which is $Q'(t) = 0.14t + 0.2$. Evaluating this at $t = 2$ years gives $Q'(2) = 0.14(2) + 0.2 = 0.48$ ppm/yr, not 0.048 ppm/yr.

An Environmental Study of a Certain Suburban Community Suggests That Q(t)=0.07t2+0.2t+2.8Q ( t ) = 0.07 t ^ { 2 } + 0.2 t + 2.8Q(t)=0.07t2+0.2t+2.8

An Environmental Study of a Certain Suburban Community Suggests That $Q ( t ) = 0.07 t ^ { 2 } + 0.2 t + 2.8$