Question

The number n of people using the elevator in an office building every hour is given by n = t2 − 10t + 40. In this equation, t is the number of hours after the building opens in the morning, 0 ≤ t ≤ 12. Will the number of people using the elevator ever be less than 15 in any one hour? Use the discriminant to answer.

Answer 1

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:  

$t^2-10t+40<15\\t^2-10t+25<0$

Now you transform the inequation back to an equation to solve it:

$t^2-10t+25=0$

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:

$D=b^2-4ac$

In this case, you have a=1, b=-10, c=25

$D= (-10)^2-4(1)(25)\\D=0$

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.