In Figure 1.107, the blue curve shows monthly mean carbon dioxide (CO2) concentration

Chapter 1, Problem 32

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In Figure 1.107, the blue curve shows monthly mean carbon dioxide (CO2) concentration, in parts per million (ppm) at Mauna Loa Observatory, Hawaii, as a function of t, in months, since December 2005. The black curve shows the monthly mean concentration adjusted for seasonal CO2 variation.98 (a) Approximately how much did the monthly mean CO2 increase between December 2005 and December 2010? (b) Find the average monthly rate of increase of the monthly mean CO2 between December 2005 and December 2010. Use this information to find a linear function that approximates the black curve. (c) The seasonal CO2 variation between December 2005 and December 2010 can be approximated by a sinusoidal function of the form Asin Bt. What is the approximate period of the function? What is its amplitude? Give a formula for the function. (d) The blue curve may be approximated by a function of the form h(t) = f(t) + g(t), where f(t) is sinusoidal and g(t) is linear. Using your work in parts (b) and (c), find a possible formula for h(t). Graph h(t) using the scale in Figure 1.107.