Answer:
The number of persons using the elevator at any hour is never going to be less that 15.
Step-by-step explanation:
To solves this you have to suppose that there are at least 15 persons on the elevator, and the equation is converted into an inequation:
[tex]t^2-10t+40<15\\t^2-10t+25<0[/tex]
Now you transform the inequation back to an equation to solve it:
[tex]t^2-10t+25=0[/tex]
You need to know if there is any negative solution for the equation, to do this you can use the discriminant for a quadratic equation:
[tex]D=b^2-4ac[/tex]
In this case, you have a=1, b=-10, c=25
[tex]D= (-10)^2-4(1)(25)\\D=0[/tex]
Since the discriminant is 0 and a<0 the equation always is going to be positive. Therefore, the number of persons using the elevator at any hour is never going to be less than 15.
