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You have just opened a new dance club, Swing Haven, but are unsure of how high to set the cover charge (entrance fee). One week you charged $4 per guest and averaged 80 guests per night. The next week you charged $10 per guest and averaged 44 guests per night. (a) Find a linear demand equation showing the number of guests q per night as a function of the cover charge p.

Answer :

Answer:

[tex]q = -6p + 104[/tex]

Step-by-step explanation:

Linear function:

A linear function has the following format:

[tex]q = mp + b[/tex]

In which m is the slope and b is the q-intercept.

One week you charged $4 per guest and averaged 80 guests per night. The next week you charged $10 per guest and averaged 44 guests per night.

This means that we have these following points: (4,80), (10,44).

Finding the slope:

With a pair of points, the slope is given by the change in q divided by the change in p.

Change in q: 44 - 80 = -36

Change in p: 10 - 4 = 6

Slope: [tex]m = \frac{-36}{6} = -6[/tex]

So

[tex]q = -6p + b[/tex]

Finding b:

We replace one of the points. Replacing (4,80).

[tex]q = -6p + b[/tex]

[tex]80 = -6*4 + b[/tex]

[tex]b = 104[/tex]

So

[tex]q = -6p + 104[/tex]

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