Question

An environmental study of a certain suburban community suggests that its average daily level of carbon monoxide will be 𝐶(𝑓) = √0.5𝑝 2 + 17 Parts per million when the population is p thousand. It is estimated that t years from now, the population of the community will be 𝑝(𝑡) = 3.1 + 0.1𝑡 2 thousand. At what rate will the carbon monoxide level be changing with respect to time 3 years from now?

Answer 1

$C(p) = \sqrt{0.5}p^2+17\\ p(t) = 3.1+0.1t^2\\ C(p(t)) = \sqrt{0.5} (3.1+0.1t^2)^2 +17 = \sqrt{0.5}(9.61+0.62t^2+t^4)+17=\\ C'(p(t)) = \sqrt{0.5}(4t^3+1.24t)\\ C'(p(3)) = 76.36+2.63=78.99$