An average of 5000 people visit an amusement park each day in the summer. The admission fee is $50. Consultants predict that, for each $2 increase in the admission fee, the park will lose an average of 250 customers each day. Determine the revenue function.

A) [tex] R(x) = -500x^2 - 2500x + 250000 [/tex]
B) [tex] R(x) = -240x + 5050 [/tex]
C) [tex] R(x) = -252x + 4950 [/tex]
D) [tex] R(x) = -125 + 11250 [/tex]

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What is the maximum value of [tex] f(x) = a \sin(k(x - d)) + C [/tex]?

A) [tex] -|a| + C [/tex]
B) [tex] |a| + C [/tex]
C) [tex] a - C [/tex]

The revenue function represents the total amount of money the amusement park makes on a given day.
Since the admission fee is $50 and the number of visitors is 5000, the initial revenue is $50 * 5000 = $250,000.
For each $2 increase in the admission fee, the park loses 250 customers, resulting in a revenue decrease of $2 * 250 = $500.
Therefore, the revenue function can be calculated using the equation R(x) = -500x + 250000, where x represents the number of $2 increases in the admission fee.

The maximum value of f(x) = a sin(k(x - d)) + c represents the maximum value of a sin function.
The maximum value of a sin function is equal to a + c, where a is the amplitude of the sine function and c is the vertical shift. The other parameters, k and d, do not affect the maximum value.
Therefore, the maximum value of the function is |a| + c.

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