Hi there!
a.
To find the total amount of people that have ENTERED by t = 20, we must take the integral of the appropriate function.

Evaluate using a calculator:

b.
To solve, we can find the total amount of people that have entered of the interval and subtract the total amount of people that have left from this value.
In other terms:

We can evaluate using a calculator (math-9 on T1-84):


c.
If:

Then:

Evaluate at t = 20:


This means that at t = 20, there is a <u>NET DECREASE</u> of people at the movie theater of around 20.823 (21) people per hour.
d.
To find the maximum, we must use the first-derivative test.
Set S(t) - R(t) equal to 0:

Graph the function with a graphing calculator and set the function equal to y = 0:
According to the graph, the graph of the first derivative changes from POSITIVE to NEGATIVE at t ≈ 17.78 hours, so there is a MAXIMUM at this value.
<u>Thus, at t = 17.78 hours, the amount of people at the movie theater is a MAXIMUM.</u>
Answer:
i do not know what i would do if i was you- ppppppproooooobably have an anxiety attack ngl
Explanation:
hey, but thanks for the free points and maybe try thinking about what will happen AFTER that horrible time
so instead of thinking about all the children coughing and wiping their boogers on their sleeves-
think about what will happen after the event- like watching net flix with a floofy blanket
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