The function n(t)=100-36^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 of 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.
We are given the function `n(t)=100-36^t ` where n is the number of free tickets remaining t hours after an e-mail is sent.
A. `n(0)=100-36^0=100-1=99 ` . This is the initial number of free tickets available.
B. n(t)=0 is the time when the number of free tickets remaining is zero. Here n(t)=0 gives :
`0=100-36^t ==> 36^t=100`
` ` So `t~~1.285 ` . There will be no free tickets after about 77 minutes.
C. Here `0<=n<=99 ` where `n in NN ` (n a natural number).
Also `0<=t<78 ` with t in minutes or `0<=t<1.285 ` ` `with t in hours. After 1.285 hours, the function is identically zero, so it no longer lies on the given model. (The number of tickets cannot be negative.)