Rebecca buys a new couch for $1,200. She plans on making a monthly payment of $75 on the balance, starting the month after she buys the couch. Which recursive function models the amount of money Rebecca still has to pay for the couch?

The recursive function is A(t + 1) = A(t) - 75

Where;

A(t) = 1,200 - 75×t

The known parameter are;

The amount Rebecca buys the new couch = $1,200

The amount she plans to make as monthly payment = $75

The time she plans to start paying = The month after she buys the couch

Strategy;

Define a recursive function that models the amount of money Rebecca still has to pay

Definition

A recursive function is one which has its own process as an input in the process of its implementation

A recursive function that models the amount of money Rebecca still has to pay for the couch is found as follows;

The amount left for her to pay in the present month = The amount left to pay in the previous month - $75

Let A(t + 1) represent the amount left for her to pay in the present month and let A(t) represent the amount left to pay in the previous month, we get;

A(t) = 1,200 - 75×t

A(t + 1) = 1,200 - 75×t - 75 = A(t) - 75

The recursive function is A(t + 1) = A(t) - 75

The function is recursive because, the function, A(t), is called in as an input to the execution of the function

Learn more about recursive functions here;

f(1) = 1,200

f(n) = f(n-1) -75 for n > 2

Step-by-step explanation:

Since the initial loan amount is $1,200, f(1) =1200.

And since $75 is deducted from the balance each month starting with n >2 , the common difference, d, is  -75 .

Use the general recursive function for an arithmetic sequence,f(n)= f (n - 1 ) +d , for n > 2 to write the recursive function models Rebecca’s situation: