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Four groups of 80 or more people a charter bus come determines the rate per person according to the formula R(n) = 8-0.05 (n-80) where n represents the number of people and R represents the rate in dollars charged to each customer. a. Find each value and interpret it in context R(75)= R(85)= b. Why is R(75)>R(85) in this context?

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Answer:

When there are fewer people, each person pays a slightly higher rate, and when there are more people, each person pays a slightly lower rate due to how the formula is constructed.

Explanation:

Let's break this down step by step.

The formula given to determine the rate per person is:

R(n) = 8 - 0.05(n - 80)

where:

R(n) represents the rate in dollars charged to each customer.

n represents the number of people.

a. Find each value and interpret it in context:

R(75):

Plug in n = 75 into the formula:

R(75) = 8 - 0.05(75 - 80)

R(75) = 8 - 0.05(-5)

R(75) = 8 + 0.25

R(75) = 8.25 dollars per person

Interpretation: If there are 75 people, the rate charged to each customer is $8.25.

R(85):

Plug in n = 85 into the formula:

R(85) = 8 - 0.05(85 - 80)

R(85) = 8 - 0.05(5)

R(85) = 8 - 0.25

R(85) = 7.75 dollars per person

Interpretation: If there are 85 people, the rate charged to each customer is $7.75.

b. Why is R(75) > R(85) in this context?

The reason R(75) is greater than R(85) in this context is because of the way the formula is structured. The formula R(n) = 8 - 0.05(n - 80) includes a term that subtracts 0.05 times the difference between the number of people (n) and 80 from the base rate of $8.

When there are fewer people (75), the subtraction term (0.05 times -5) results in an addition to the base rate, making the rate per person slightly higher ($8.25). However, when there are more people (85), the subtraction term (0.05 times 5) results in a deduction from the base rate, making the rate per person slightly lower ($7.75).

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