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).