Suppose that r(t) = r0 * e^(-kt) with k > 0, is the rate at which a nation extracts oil where r0=10^7 barrels/year is the current rate of extraction. Suppose also that the estimate of the total oil reserve is 2*10^9 barrels. a. Find Q(t), the total amount of oil extracted by the nation after t years. b. Evaluate lim(t->infinity)Q(t) and explain the meaning of this limit. c. Find the minimum decay constant k for which the total oil reserves will last forever. d. Suppose r0=2*10^7 barrels/yr and the decay constant k is the minimum value found in part c. How long will the total oil reserves last?