A new smog-control device will reduce the output of sulfur oxides from automobile exhausts. It is estimated that the rate of savings (in millions of dollars per year) to the community from the use of this device will be approximated by S′(t)= -t² + 4t + 8, after t years of use of the device. The new device cuts down on the production of sulfur oxides, but it causes an increase in the production of nitrous oxides. The rate of additional costs (in millions of dollars per year) to the community after t years is approximated by

(a) For how many years will it pay to use the new device?
(b) What will be the net savings over this period of time?

Transcribed Image Text:

C' (t) 3 25 1².