A particle of mass tn moving through a fluid is subjected to a viscous resistance R, which is a function of the velocity v. The relationship between the resistance R, velocity v, and time t is given by the equation cu(r) t in 'i'('o) R(u) du. Suppose that R{v) vjv for a particular fluid, where R is in newtons and u is in meters per second. If m 10 kg and i;(0) = 10 m/s, approximate the time required for the particle to slow to v = 5 m/s

L16 - 9 3) Find the actual cost of producing the 101st item given C(101) = 1000 + 25(101) − 0.1(101) =2 04 .90. Now suppose that the unit price p at which x items will sell can be modeled by the demand function p(x)= −0.3x +1 2,0 ≤ x ≤ 400. 4) Find the revenue from the sale of x items. 5) Find the proﬁt function, P(x), which gives the proﬁt from the sale of x items. 6) Estimate the marginal proﬁt when 50 items are sold. Note: P(51) − P(50) = 3579.80 − 3500.