A nation's population (to the nearest million) was 280 million in 2000 and 310 in 2010. It is projected that the population in 2050 will be 437 million. To construct a logistic model, both the growth rate and the carrying capacity must be estimated. There are several ways to estimate these parameters. Use parts (a) through (f) to use one approach. a. Assume that t=0 corresponds to 2000 and that the population growth is exponential for the first ten years; that is, between 2000 and 2010, the population given by P(t) = P(0) e". Estimate the growth rate r using this assumption. (Round to five decimal places as needed.) b. Write the solution of the logistic equation with the value of r found in part (a). Write any populations in the logistic equation in millions of people. c. Use the projected value P(50) = 437 million to find a value of the carrying capacity K. (Type an integer or decimal rounded to the nearest hundredth as needed.)