8.Suppose that the population,P, of China (in billions) can be approximated by the function P(t)=1.15(1.014)t where t is the number of years since the start of 1993.

a. According to the model, what was the total change in the population of China between January 1, 1993 and January 1, 2000? What will be the average rate of change of the population over this time period? Is this average rate of change greater or less than the instantaneous rate of change of the population on January 1, 2000? Explain and justify, being sure to include proper units on all your answers.

b. According to the model, what is the average rate of change of the population of China in the ten-year period starting on January 1, 2012?

c. Write an expression involving limits that, if evaluated, would give the exact instantaneous rate of change of the population on today's date. Then estimate the value of this limit (discuss how you chose to do so) and explain the meaning (including units) of the value you have found.

d. Find an equation for the tangent line to the function y=P(t) at the point where the t-value is given by today's date.