Chapter 6.1, Problem 54E

 Carbon uptake An important process in the study of global warming and greenhouse gases is the net ecosystem exchange, which is the rate at which carbon leaves an ecosystem and enters the atmosphere in a particular geographic region. Let N(t) equal the net ecosystem exchange on an average July day in a high-altitude coniferous forest, where N(t) is measured in grams of carbon per square meter per hour and f is the number of hours past midnight so that 0 ≤ t ≤ 24 (see figure). Negative values of N correspond to times when the amount of carbon in the atmosphere decreases, and positive values of N occur when the amount of carbon in the atmosphere increases.

  a.    Trees and other plants help reduce carbon emissions in the atmosphere by using photosynthesis to absorb carbon dioxide and release oxygen Give a possible explanation why N is negative on the interval 5 < t < 17.

  b.    The cumulative net carbon uptake, ${\displaystyle {\int }_0^{24}N\left(t\right)dt}$, is the net change in the amount of carbon in the atmosphere over a 24-hour period in the coniferous forest Use a midpoint Riemann sum with n = 12 subintervals to estimate the cumulative net carbon uptake in the coniferous forest and interpret the result