Swimming pool hours: A swimming pool opens at 8 A.M. and closes at 6 P.M. In summertime, t...

Swimming pool hours: A swimming pool opens at 8 A.M. and closes at 6 P.M. In summertime, the number of people in the pool at any time can be approximated by the formula S(t) = − t2 + 10t, where S is the number of swimmers and t is the number of hours the pool has been open (8 a.m.: t = 0, 9 a.m.: t = 1,10 a.m.: t = 2, etc.).

a. How many swimmers are in the pool at 6 p.m.? Why?

b. Between what times would you expect the largest number of swimmers?

c. Approximately how many swimmers are in the pool at 3 p.m.?

d. Create a table of values for t = 1, 2, 3,4, … and check your answer to part b.