(Please show me how you solved this!!)

Question

The rate r(t) at which forest is burned in a forest fire, t hours is given in the tabs after the start of the fire.
t(hours) 0 3 6 9,
r(t) (acres/hour) 5 9 14 16.
The amount of forest burned in the first nine hours has:
(A) a lower estimate of 28 acres and an upper estimate of 39 acres.
(B) a lower estimate of 14 acres and an upper estimate of 23 acres.
(C) a lower estimate of 70 acres and an upper estimate of 115 acres.
(D) a lower estimate of 115 acres and an upper estimate of 150 acres.
(E) a lower estimate of 84 acres and an upper estimate of 117 acres.

Answer 1

since the chart shows the rate of burn, the amount burned is the area under the graph. Since the curve is concave down, using left-side rectangles will over-estimate the area. That is, using 3 intervals of width 3,
3(f(0)+f(3)+f(6))
The right-side estimate is an under-estimate: 3(f(3)+f(6)+f(9))

Better review Riemann sums.