The population of elk in a national park is given by the function 1000 P(t) = 1+15e-3t where t is the time in decades since 1960. Calculate P'(3). What does it represent? What will happen to the elk population in the long run? Justify your answer.

The total expenditures (in millions) of current dollars for pollution abatement and control during the period from 2000 through 2019 can be approximated by the function P(x) = 166.61 e 0.03x, where x = 0 corresponds to the year 2000. (a) In what year would the total expenditures reach $208 million dollars? (b) If this model remains accurate, when would the total expenditures reach $482 million? (a) The expenditures would reach $208 million in the year mid- (Simplify your answer. Type a whole number.)

In 2010, the population of a country was 53 million and growing at a rate of 1.7% per year. Assuming the percentage growth rate remains constant, express the population, P, in millions, as a function of t, the number of years after 2010. P = f(t) = [ million people help (formulas)

According to the U.S. Census Bureau, the population of the United States in 2008 was 304 million people. In addition, the population of the United States was growing at a rate of 1.1% per year. Assuming this growth rate continues, the model t – 2008 P(t) = 304 · (1.011)* represents the population P (in millions of people) in year t. According to the model, when will the population be 366 million people? Be sure to round your answer to the nearest whole year. Year