Question

The Philly Tour Company is planning on bringing bottles of water on their bus tour. The number of bottles will be based on how many people take the tour using the function:

b(n)=3n+5

where π is the number of people taking the tour and b is the number of water bottles the Philly Tour Company will bring. A bus tour will have a minimum of 4 people and a maximum of 15 people.

Give sets that describe the domain and range of the function above. Explain how you arrived at your sets.

Answer 1

The domain and range for the function b(n)=3n+5, which represents the number of water bottles brought on a bus tour based on the number of people, are determined. The domain is {4, 5, 6, ..., 15} for the 4 to 15 people on the tour, and the range is {17, 20, 23, ..., 50} for the corresponding water bottles calculated.

Step-by-step explanation:

The student's question involves finding the domain and range for a function b(n)=3n+5, given that the number of people on the bus tour is between 4 and 15. To determine the domain, we look at the possible values for n (the number of people), which in this case range from 4 to 15. Thus, the domain represents these values and can be set as {4, 5, 6, ..., 15}.

Next, to find the range of the function, we calculate the number of water bottles for each number of people within the domain using the given function. For the minimum number of people n=4, the function gives us 3(4)+5=17 bottles, and for the maximum number of people n=15, it gives us 3(15)+5=50 bottles. Hence, the set for the range includes all possible numbers of bottles the company will bring on the tour given the function, which is {17, 20, 23, ..., 50}, calculated for each value in the domain.