Question 11. A manufacturer of electronic equipment requires a certain rare metal. They have a reserve supply 4,000,000 units that they will not be able to replace. If the rate at which the metal is used is given by f(t) = 100000e ., where t is time (in years), how long will it be before they use up the supply? Question 12. Suppose a company wants to introduce a new machine that will produce a rate of annual savings (in dollars) given by S'(t) = 150-x2, where x is the number of years of operation of the machine, while producing a rate of annual costs (in dollars) of C'(x) = x2 + 4x. For how many years will it br profitable to use this new machine? What are the net total savings over the entire period of use of the machine? 150 - 1= 149 TOP 1+ 4 = Bottom 150 -x = x tux 72+4 x - 150 0= 2*+4 - 6 = / (b ) 2 - 4 ( 4) ( x ) 2 a - H IV ( # ) ( 4( 2 ) 6-150 2 (2) 57 1202.75 - 9. 358 or 7,983 4Question 13. The yearly rate of consumption of natural gas (in trillions of cubic feet) for a certain city is C'(t) = t + 20.olt where t is the time in years and t = 0 corresponds to 2000. At this consumption rate, what was the total amount the city used in the 10 year period from 2000 to 2010? Question 14. Find the revenue function for marginal revenue function R'(x) = 600 - 50.0002x. What is the demand function? Question 15. Find the cost function for the marginal cost function C'(x) = a +-, 2 units is $5.50. + 72 given that the cost to make