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>
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Answer:
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The independent variable is psychotherapy while the dependent variable is the people.
<h3>The types of variables.</h3>
In an experiment, there are two (2) main types of variables and these include the following:
<h3>What is an independent variable?</h3>
An independent variable can be defined as the variable that is being manipulated by an experimenter or researcher. This ultimately implies that, it is typically considered to be the cause in an experiment and it stands alone because it cannot be changed by any variable being observed or measured.
<h3>What is a dependent variable?</h3>
A dependent variable can be defined as the variable which signifies the effect of an independent variable and it is dependent on other factors because it's the part of an experiment that's being observed or measured.
Based on the information provided about this experiment, we can infer and logically deduce that the independent variable is psychotherapy while the dependent variable is the people.
Read more on dependent variable here: brainly.com/question/25223322
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