A parking lot charges a fixed fee of Rs. 40 for any stay up to and including 2 hours. For every additional hour or part thereof, an extra Rs. 15 per hour is charged. No vehicle is allowed to remain inside for more than 8 hours at a stretch.
Let C(t) denote the total parking charge (in rupees) for a car that remains in the lot for t hours, where 0<t≤8.
a. (i) Express C(t) as a piecewise-defined algebraic rule in terms of t. Show the intervals of t for which each rule applies.
b. (ii) Explain why C qualifies as a function of t for the stated interval of stay.
c. (iii) State the domain and the range of C in set–builder form.
d. (iv) Comment on the reasonableness of extending this function beyond the stated interval 0<t≤8. Give one mathematical and one practical argument.