In Figure 1.120, 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.

(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 A sin 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 1.120.

Transcribed Image Text:

ppm 395 390 385 380 375 12 Ax 24 36 48 60 Figure 1.120 t(months since Dec 2005)