Question

A movie theater is filled to capacity with 650 people. After the movie ends, people start leaving at the rate of 100 each minute.

For what values of t does the equation make sense in practical terms.
Domain=?

Answer 1

try and write an equation for the number of people in the movie theatre as a function of time.

Answer 2

once you have done that, you need to think about the equation. will people still be leaving the theatre, when no one is in it?

Answer 3

N=650-100t
this is my equation for the number of people in the theater. Would the domain just be (0,infinity)?

Answer 4

how many people would be at the theatre at t = 10?

Answer 5

according to your function.

Answer 6

It would be a negative number which isnt possible. The highest whole number to not be negative is 6

Answer 7

well first of all, minutes do not need to be whole. you can have 6.5 minutes.

Answer 8

the question asked on what domain the equation makes sense in practical terms. a negative number of people does not sound very practical to me. so write the domain where it does make sense.

Answer 9

would it be (0,6.5] then?

Answer 10

almost. why do you say (0,6.5] instead of [0,6.5]? nothing is wrong with your equation at t=0.

Answer 11

oh okay got it. Thanks for your help!