See table below. A grain elevator fills each railcar of a train with grain. The number of railcars filled after t hours is given by a differentiable function R for 0 ? t ? 15. Values of R(t) at various times t are given in the table above.

a) Use the data in the table to approximate the rate at which the number of filled railcars is changing at time t = 5. Show the computations that lead to your answer. Indicate units of measure.

b) Will the instantaneous rate at which the number of filled railcars is changing at some time t be equal to the approximation in part (a)? Justify your answer.

c) Use a right Riemann sum with the four subintervals indicated in the table to estimate 1 ?15 R(t)dt. 15 0

Using correct units, interpret the meaning of 1 ?15 R(t)dt in the context of this problem. 15 0

d) Determine ?10 R'(t)dt. Using correct units, explain the meaning of the expression in the context of 2

this problem.