1. Find the number of years that the estimated petroleum reserves would last if used at the same rate as in the base year.
2. How long would the estimated petroleum reserves last if the growth constant was only 2% instead of 4.7%?

In Exercises, estimate the length of time until depletion for each mineral.

3. Bauxite (the ore from which aluminum is obtained): estimated reserves in base year, 15,000,000 thousand tons; rate of consumption in base year, 63,000 thousand tons; growth constant, 6%
4. Bituminous coal: estimated world reserves, 2,000,000 million tons; rate of consumption in base year, 2200 million tons; growth constant, 4%

5. (a) Verify that the function k(t) defined previously has the right values at t = 0 and t = 50.

     (b) Find a similar function that has k(0) = 0.03 and k(50) = 0.02.

6. (a) Use the function you defined in Exercise 5

(b) to write an integral for world petroleum consumption from 1970 until T years after 1970.  Trying various values of T and using a numerical integrator, we find that according to this model the current reserve of 3,000,000 million barrels will be exhausted in about 77 years from 1970, that is, in about 2047.