Question

(minutes) g(t) (cubic feet per minute) 12.8 15.1 20.5 18.3 22.7 Grain is being added to a silo. At time 1 = 0, the rate at which grain is being added is modeled by the differentiable function g, where g() is measured in cubic feet per minute for Os138 minutes. a. Write an integral expression that represents the total amount of grain added to the silo from time 10 to time 1 8. Use a right Riemann sum with the four subintervals indicated by the data in the table to approximate the integral. b. The grain in the silo is spoiling at a rate modeled by w(t) = 32 sin (1) where w(t) is measured in cubic feet per minute for 05138 minutes. Using the result from part (a), approximate the amount of unspoiled grain remaining in the silo at time 1 = 8. c. Based on the model in part (b), is the amount of unspoiled grain in the silo increasing or decreasing at time 1 - 6? Show the work that leads to your answer. d. Chloe rides her bike for 4 hours through a park. Her velocity is described by the function below. At time 1-3, is Chloe speeding up or slowing down. Explain your reasoning. te- for 0 <t<2 1) 112 - 3t - 2 for 2 <t < 4.

Answer 1

2 As alt gives rate of chanse in grain ad dihin. Total amount of grain added bror to to t=8 a= So g (t) at

de perding on data sires in no table we have to divide lokal inkoval [08] into baro interval on [] [15], [5,6] and [68] As we have to use right riemon Sun so we will take values on st) at right ead. point on each carora none & legltat = (1-0) + 8) + (5-1) + Hs). - (6-5), f(6) + (8-6) + 48) - 1x 15.1 + 4* 20.5+ 1* 18.3+2*22-3 = 15.1 +82 + 18 3 + 45.4. = 1608 A Ans total amount ao srain at t=8

grair is spoilis at a rate or w(t) = 32. Sin (177) Tohl amount of grain spoiled at time t=8 )= لا لے یا دما - 38 3erson (1 h) at - 32 Sidson (1 h) dt [By marcial -3221-0977675 eu tt lok station rhJศ. vcrire does no- erist

W = 35. 12856 en So waspiled grain abter +=8 2 يا لا = 160.8 - 35.12856 en = 125.67144 H at end of +=8 , unspoilled grain = 125.67144 cut ta) is increasio ir f.(2) 70 and detocasa it di(n)co. Here it to be yo amor of spoiled srain is WLt) W(= W' (t)= 32 sin(at) at t= 6 W 6) = 325 Sonesia = 16.86317 alt=6 rate at which goain added 916) – 19.3. so vale at colich up spolled grain chansing. at t=0 - 916 - (6) - 18.30-16.06317 = 2.2368 ooo A vale at wlich an spoiled grain charging is Pasitice. So amant d unspoiled grain is increasing.