A conservation agency monitors the amount of nitrate (in milligrams per liter) dissolved in a stream. Let N(t) denote the nitrate concentration t days after monitoring begins. Selected measurements are shown in the table below.
t (days)
0
10
20
30
N(t) (mg/L)
4.8
5.5
6.3
7.4
Laboratory analysis additionally reports that N′(15)=0.09 (mg/L)/day.
(1) Estimate the average rate of change of the nitrate concentration over the first 20 days. Include appropriate units.
(2) Interpret the meaning of the value N′(15)=0.09 in the context of the stream. Include units and comment on the sign of the quantity.
(3) Compare the magnitude of your estimate in part (a) with the instantaneous rate in part (b). Describe what this comparison implies about how the nitrate concentration is changing during the first 20 days.