# 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...

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*.

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### 1 Answer

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.)