. Improper Integral in Use

9. Refer to the previous exercise. Suppose that car-washing machine will generate infinite continuous income stream. In such case, what is the present value of it? 10. The owner of a local cinema is considering two alternative plans for renovating and improving the theater. Plan A calls for an immediate cash outlay $250000, whereas plan B requires an immediate cash outlay of $130000. It has been estimated that adopting plan A would result in an infinite net income stream generated at the rate of f(t ) =0,5t thousand dollars per year, whereas adopting plan B would result in an infinite net income stream generated at the rate of g(t ) =0,4t thousand dollars per year. If the prevailing discount rate is 5% per year, compounded continuously, which renovation and improving plan is more beneficial to the owner? Why? 11. Camila plans to expand her business, and her expansion plan requires one-time investment of 100000 euros. Also, she estimates that business expansion would generate a net income stream f (t) =0,24t thousand euros t years from expansion. If the prevailing discount rate is 4% per year, compounded continuously, what is the present value of the investment? Should she go ahead with her expansion plan? Why