The burning of fossil fuels releases greenhouse gases (roughly 60% carbon dioxide) into the atmosphere. In 2010, the United States released approximately 5.8 billion metric tons of carbon dioxide (Environmental Protection Agency estimate), while China released approximately 8.2 billion metric tons (U.S. Department of Energy estimate). Reasonable estimates of the growth rate in carbon dioxide emissions are 4% per year for the United States and 9% per year for China. In 2010, the U.S. population was 309 million, growing at a rate of 0.7% per year, and the population of China was 1.3 billion, growing at a rate of 0.5% per year.

a. Find exponential growth functions for the amount of carbon dioxide released by the United States and China. Let t = 0 correspond to 2010.

b. According to the models in part (a), when will Chinese emissions double those of the United States?

c. What was the amount of carbon dioxide released by the United States and China per capita in 2010?

d. Find exponential growth functions for the per capita amount of carbon dioxide released by the United States and China. Let t = 0 correspond to 2010.

e. Use the models of part (d) to determine the year in which per capita emissions in the two countries are equal.