The number 'N' of cars produced at a certain factory in 1 day after 't' hours of operation is given by N(t)=100t-5t^2, 0< or equal t < or equal 10. If the cost 'C' (in dollars) of producing 'N' cars is C(N)=15,000+8000N, find the cost 'C' as a function of the time 't' of operation of the factory Then Interpret C(t) when t=5 hours as a new function.

Answer:We know that: [tex]C_{(N)}=15000+8000N[/tex]So first we need to substitute the next equation in the C(N) equation[tex]N_{(t)} = 100t-5t^{2}[/tex]And therefore we have:[tex]C_{(t)}=15,000 + 8000*(100t-5t^{2})\\C_{(t)}=15,000 + 800000t-40000t^{2}[/tex]Finally we replace at t = 5 in the equation above and we have:[tex]C_{(5)}=15,000 + 800000*5-40000*5^{2}\\C_{(5)}= 3015000[/tex]The interpretation is that after 5 hours of operation, we have wasted 3015000 dollars producing cars.