remaining at the service center in a college student t hours after an email is sent to the student body A:what does n(0) mean? calculate the function value of t for which n(t) =0 and B:what does n(t) =0 mean? calculate the value of t for which n(t)=0 explain any restrictions on n and t
A. The value n(0) means that at the beginning there were 100 free tickets (before the email was sent).
Solve the equation: 100 - 36t^2 = 0; t^2 = 100/36 = 25/9; t = sqrt(25/9) = 5/3 hours = 1 hour 40 minutes. The second solution is t = -5/3 that does not make sense.
B. We found the value of t = 1 hour 40 minutes after which there will be no free tickets left.
There are the following restrictions: 0 <= n <= 100 (the number of free tickets is no more than their initial number 100 and no less than 0); 0 <= t <= 5/3 because for t > 5/3 the number of free tickets is 0 and does not satisfy the formula n(t) = 100 - 36t^2. On the other hand, negative values of t may be interpreted as the moments before the email was sent, however, the formula again cannot be true.