Question

The given function models the number of cars that are put through a quality control test each hour at a car production factory. Some cars are kept overnight at the quality control facility, while some cars arrive at different times of the day.
c(t)=-2^t+8t+20

For how many hours does the quality control facility operate each day?

The best form of the equation for finding the required information is_____ . The quality control facility operates for______ hours each day.

Answer 1

hours each day.

Step-by-step explanation:

The given function models the number of cars that are put through a quality control test each hour at a car production factory.

The given function is

We need to find the number of hours does the quality control facility operate each day.

Rewrite the given function it factored form.

Taking out the common factors from each parenthesis.

The factored form of given function is c(t)=-(t-10)(t+2).

Equate the function equal to 0 to find the x-intercept.

Number of hours cannot be negative. So from t=0 to t=10 quality control facility operate the cars.

Therefore the quality control facility operates for 10 hours each day.

Answer 2

Answer:

The best form of the equation for finding the required information is factored form. The quality control facility operates for 10 hours each day.

Explanation:

$\displaystyle [-t^2 - 2t] + [10t + 20] \\ -t[t + 2] \: \: \: 10[t + 2] \\ \\ -[t - 10][t + 2]$

Time is ALWAYS POSITIVE, so we ONLY want the NON-NEGATIVE root.

I am joyous to assist you anytime.