Jovanna gives a walking tour of a popular tourist city to one person for $31. To increase her business, she would lower the price by $2 per person for each additional person. Write the cost per person c as a function of the number of people n on the tour. How much does she make for a tour with 16 people?

Write the cost per person c as a function of the number of people n on the tour.

(n,c) ... (1,31)

cost per person (c) decreases by $2 for each additional person ... slope

c = - [2 (n - 1)] + 31

n = 16 people.

C = 31- 2(n-1) = 31 - 2(16-1) = 31 - 30 = $1.00 per person.
16 * 1 = $16. = Amt. made.

To write the cost per person c as a function of the number of people n on the tour, we need to determine the relationship between the number of people and the cost per person.

Since the price decreases by $2 per additional person, we can determine the cost per person as follows:

For the first person, the cost is $31.
For the second person, the cost is $31 - $2 = $29.
For the third person, the cost is $31 - ($2 * 2) = $27.
For the fourth person, the cost is $31 - ($2 * 3) = $25.

By observing this pattern, we can see that the cost per person decreases linearly as the number of people increases. The difference in cost per person per additional person is $2.

Therefore, we can express the cost per person c as a function of the number of people n as follows:

c(n) = $31 - ($2 * (n-1))

Next, let's find out how much she makes for a tour with 16 people:

To calculate the total amount she makes for a tour with 16 people, we need to multiply the cost per person by the number of people.

For a tour with 16 people:
c(16) = $31 - ($2 * (16-1))
c(16) = $31 - ($2 * 15)
c(16) = $31 - $30
c(16) = $1

Since the cost per person is $1, we can multiply it by the number of people to find out how much she makes:

Total amount = cost per person * number of people
Total amount = $1 * 16
Total amount = $16

Therefore, she makes $16 for a tour with 16 people.