Audrianna gives a walking tour of a popular tourist city to one person for $ 49. 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 19 people?

The price for one person is $ 49. For every extra person, Audrianna lowers the price by $ 2. Thus, it is necessary to create a function where cost (C) will vary according to the variation in the number of people (N).

For more than one person, we must put variable C as a function of the variation in the number of people. However, we want to find the price. To find the price for each extra person, simply decrease the one-person value ($ 49) of the discount ($ 2) multiplied by the total number of people (N).

Thus, we have the following function: C = 49 - 2 (N)

For one more person: C = 49 - 2 (1) = $ 47

For two more people: C = 49 - 2 (2) = $ 45

( ...)

For nineteen more people: C = 49 - 2 (19) = $ 11

So if nineteen people participate in the tour, the cost for each person will be $ 11.