50. Steve borrows $4,800 from his parents to purchase a used car. No interest is charged on the loan and Steve will pay his parents $150 per month until the loan is paid off.
(a)Write a function that describes the relationship between the amount Steve owes his parents and the number of months since the loan was made.
(b)What are the domain and range of the function in part (a)? What do these represent in context of the situation?
(a) The relationship between the amount Steve owes his parents and the number of months since the loan was made can be described with the following function:
Let x represent the number of months since the loan was made.
Let y represent the amount Steve owes his parents.
The initial loan amount is $4,800, and Steve pays $150 per month. So, for each month that passes, the amount Steve owes decreases by $150. Therefore, the function can be defined as:
y = 4800 - 150x
(b) The domain of the function is the set of possible inputs, which in this case is the number of months since the loan was made. Since the loan is being paid off, it would not make sense to have negative months, so the domain would be non-negative integers.
Domain: x ≥ 0
The range of the function is the set of possible outputs, which in this case is the amount Steve owes his parents. This can take any value from the initial loan amount ($4,800) down to $0 as Steve pays off the loan.
Range: 0 ≤ y ≤ 4800
In the context of the situation, the domain represents the valid number of months since the loan was made, while the range represents the valid amount Steve can owe his parents at any given time.
y = 4800 - 150x
since the loan balance must be positive
range: [0,4800]
domain: [0,36]