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 $Q ( t ) = 0.07 t ^ { 2 } + 0.6 t + 2.8$ parts per million (ppm). The rate that the carbon monoxide level will change with respect to time 3 years from now will be 0.42 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 $Q'(t) = 0.14t + 0.6$. Evaluating this derivative 3 years from now ($t = 3$) gives $Q'(3) = 0.14(3) + 0.6 = 1.02$ ppm/yr, not 0.42 ppm/yr.

An Environmental Study of a Certain Suburban Community Suggests That Q(t)=0.07t2+0.6t+2.8Q ( t ) = 0.07 t ^ { 2 } + 0.6 t + 2.8Q(t)=0.07t2+0.6t+2.8

An Environmental Study of a Certain Suburban Community Suggests That $Q ( t ) = 0.07 t ^ { 2 } + 0.6 t + 2.8$