Question

The South Bowie Library and Oxon Hill Library are having a used book sale. The total cost, y, is a function of the number of books, X.

Cost = x + 5
a) In which library is it cheaper to buy books? Explain.
b) Which function has a greater constant rate of change? Explain.

a. South Bowie Library is cheaper to buy books because x is smaller.
b. Oxon Hill Library has a greater constant rate of change because its slope is 1.

Answer 1

Both libraries have the same prices for books and the same constant rate of change.

Step-by-step explanation:

a) To determine which library is cheaper to buy books, we need to compare the values of the constant term (the x-intercept) in the cost functions of each library. In this case, the cost function is y = x + 5, where x represents the number of books. Since the cost at South Bowie Library is $5 and the cost at Oxon Hill Library is $5 as well, both libraries have the same prices for books. Therefore, it is not cheaper to buy books at either library.

b) The constant rate of change is equal to the slope of the cost function. In this case, the slope is 1 for both libraries. Therefore, both libraries have the same constant rate of change.

Answer 2

The South Bowie Library is cheaper to buy books because it has a smaller value of x. The function Cost = x + 5 has a greater constant rate of change because its slope is 1.

Step-by-step explanation:

The total cost of books, y, is a function of the number of books, x, represented by the equation Cost = x + 5. To determine which library is cheaper to buy books, we need to compare the values of x for each library. Let's say South Bowie Library has x1 books and Oxon Hill Library has x2 books. If x1 < x2, then South Bowie Library is cheaper to buy books.

To determine which function has a greater constant rate of change, we need to compare the slopes of the functions. In the equation Cost = x + 5, the slope is 1. In this case, the slope is the rate at which the cost increases as the number of books increases. Therefore, the function with a slope of 1 has a greater constant rate of change.