Grain is being added to a silo. At time t=0, the silo is empty. The rate...

 

 
 

 

Transcribed Image Text:

Grain is being added to a silo. At time t=0, the silo is empty. The rate at which grain is being added is modeled by the differentiable function g, where g(t) is measured in cubic feet per minute for Osts8 minutes. Selected values of git) are given in the table above. (a) Using the data in the table, approximate g'(3) in the context of the problem. (b) Write an integral expression that represents the total amount of grain added to the silo from time t=0. Use a right Riemann sum with the four subintervals indicated by the data in the table nt w(t) = 32(sin to approximate the integral. (c) The grain in the silo is spoiling at a rate modeled by where w(t) is measured in cubic feet per minute for Osts8 minutes. Using the result from part (b), approximate the amount of unspoiled grain remaining in the silo at time t=8. (d) Based on the model in part (C), is the amount of unspoiled grain in the silo increasing or decreasing at time t=6? Show the work that leads to your answer. (minutes) 1 | 5 6 8 g(1) (cubic feet per minute) 12.8 15.1 20.5 18.3 22.7 Grain is being added to a silo. At time t=0, the silo is empty. The rate at which grain is being added is modeled by the differentiable function g, where g(t) is measured in cubic feet per minute for Osts8 minutes. Selected values of git) are given in the table above. (a) Using the data in the table, approximate g'(3) in the context of the problem. (b) Write an integral expression that represents the total amount of grain added to the silo from time t=0. Use a right Riemann sum with the four subintervals indicated by the data in the table nt w(t) = 32(sin to approximate the integral. (c) The grain in the silo is spoiling at a rate modeled by where w(t) is measured in cubic feet per minute for Osts8 minutes. Using the result from part (b), approximate the amount of unspoiled grain remaining in the silo at time t=8. (d) Based on the model in part (C), is the amount of unspoiled grain in the silo increasing or decreasing at time t=6? Show the work that leads to your answer. (minutes) 1 | 5 6 8 g(1) (cubic feet per minute) 12.8 15.1 20.5 18.3 22.7