The function nt 100 36t2 gives the number n of free concer

The function n(t) = 100 - 36t^2 gives the number n of free concert tickets remaining at the service counter in a college student center t hours after an email is sent to the student body. A. What does n(0) mean? Calculate the function value n(0). B. What does n(t) = 0 mean? Calculate the value of t for which n(t) = 0. Explain any restrictions on n and t.

Solution

(a) n(0) means number of tickets at the starting, that is, when an email is sent.

n(t) = 100 - 36t^2

n(0) = 100

(b) n(t) = 0 means at the time t no ticket is remaining.

100 - 36 t^2 = 0

t^2 = 100/36

t = 10/6 hours

t cannot be greater than 10/6.