Question

A music company charges an initial $85 maintenance fee and then $39 per month to rent an instrument. two students each write a function, a(n)________ , to represent the amount of money paid after a number of monthly payments

Answer 1

The function 'a(n) = 85 + 39n' represents the total amount of money paid after 'n' monthly payments for renting an instrument, where '85' is the initial maintenance fee and '39n' is the cost of renting the instrument per month times the number of months.

Step-by-step explanation:

The music company's rental cost can be represented as a linear function of the number of monthly payments. Let n be the number of monthly payments. The initial maintenance fee is a fixed cost and is only paid once, while the monthly rental fee is a variable cost that depends on n. We can create the function by adding the initial maintenance fee to the product of the number of months (n) and the per-month cost. The function a(n) to represent the total amount paid after n monthly payments is:

a(n) = 85 + 39n

The initial fee is $85, and the fee per month is $39. We simply insert these values into the linear function. When a student rents an instrument for one month, the cost is obtained by plugging in n = 1 into the function, yielding $124. Each additional month adds $39 to the total cost.