Question

At the beginning of the school year, Billy's dad deposited $100 in Billy's school lunch account. Each time Billy buys hot lunch, $4 is deducted from the account balance. The function B(h) represents the balance, in dollars, of Billy's lunch account after he buys hot lunch h times.

What is the domain of B(h)?

Answer 1

The domain of B(h) is the set of whole numbers from 0 to 25, which are the possible numbers of hot lunches Billy can buy with his initial $100, given that each hot lunch costs $4.

Step-by-step explanation:

The domain of the function B(h), which represents the balance in Billy's lunch account after he buys hot lunch h times, refers to the set of all possible values of h that make the function defined and meaningful.

Since Billy starts with $100 and each hot lunch costs $4, the function B(h) can be represented as B(h) = 100 - 4h.

The maximum number of times Billy can buy lunch is the integer quotient of the initial balance ($100) divided by the cost per lunch ($4), which is 25 times.

Therefore, the domain of B(h) is all whole numbers from 0 to 25, inclusively, because h cannot be negative (you can't buy a negative number of lunches) and Billy cannot buy more lunches than the account can fund.