Let C(n) be a city's cost, in millions of dollars, for plowing the roads when n inches of snow have fallen. Let c(n) = C' (n). Evaluate theexpression and interpret your answer in terms of the cost of plowing snow, givenc' (n) < 0,c(24) = 0.3,c (15) +241,²415f¹ c (n) dn = 7.9, c(15) = 0.7,C(15) = 9, C(24) = 13.c' (n) dn=The cost of plowing increases at the instanteneous rate of $ ifallen.million/inch after 24 inches have already

Given: Let Cn be the city's cost in millions of dollars for plowing the roads when n inches of snow have fallen. Let cn=C'n. Also, it is given that: c'n<0 , ∫015cn dn=7.9 c15=0.17 , c24=0.3 , C15=9 , C24=13 To Find: c15+∫1524c'n dn= We need to find the instantaneous rate at which the cost of plowing is increasing after 24 inches have already fallen.Fundamental Theorem of Calculus: The fundamental theorem of calculus states that if a function fx is continuous over the interval a,b and Fx is any antiderivative of the function fx, then we have: ∫abf(x) dx=F(b)-F(a)Solution: We need to calculate c15+∫1524c'n dn. Here, the antiderivative of c'n is cn i.e., cn is the antiderivative of c'n. Then, by using the fundamental theorem of calculus, we get: ∫abc'n dn=c(b)-c(a) Also, a=15 and b=24 . Then, we have: ∫1524c'n dn=c(24)-c(15) ..........1 Then, the value of c15+∫1524c'n dn will be: c(15)+∫1524c'(n) dn=c15+c(24)-c(15) [ Using equation 1 ] c(15)+∫1524c'(n) dn=c15+c(24)-c(15) c(15)+∫1524c'(n) dn=c15+c(24)-c(15) c(15)+∫1524c'(n) dn=c(24) Since c24=0.3, therefore, we get: c(15)+∫1524c'(n) dn=0.3 Hence, the instantaneous rate at which the cost of plowing is increasing after 24 inches have already fallen is $0.3 million/inch.Answer: c(15)+∫1524c'(n) dn= 0.3 The cost of plowing increases at the instantaneous rate of $ 0.3 million/inch after 24 inches have already fallen.