Answer to Question #320378 in Calculus for koi

Question #320378

An environmental study of a certain suburban community suggests that its average daily level of carbon monoxide will be 𝐢(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(𝑑) = 3.1 + 0.1𝑑 2 thousand. At what rate will the carbon monoxide level be changing with respect to time 3 years from now?


1
Expert's answer
2022-04-03T15:23:14-0400

C(p)=0.5p2+17p(t)=3.1+0.1t2C(p(t))=0.5(3.1+0.1t2)2+17=0.5(9.61+0.62t2+t4)+17=Cβ€²(p(t))=0.5(4t3+1.24t)Cβ€²(p(3))=76.36+2.63=78.99C(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


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