Question

fernando borrowed money from the bank to buy a used car. the total amount owed is $7,200. fernando will make 36 monthly payments of $200 in order to pay off the loan. the function a(m) represents the amount fernando still owes, in dollars, after making m payments.
what is the range of a(m)?
all multiples of 36 from 0 to 7,200
all real numbers from 0 to 7,200
all whole numbers from 0 to 7,200
all multiples of 200 from 0 to 7,200

Explanation:

Step1: Analyze the function

The function \(A(m)=7200 - 200m\).

Step2: Find the values of \(A(m)\)

When \(m = 0\), \(A(0)=7200-200\times0 = 7200\).
When \(m = 1\), \(A(1)=7200-200\times1=7000\).
When \(m = 2\), \(A(2)=7200 - 200\times2 = 6800\).
\(\cdots\)
When \(m = 36\), \(A(36)=7200-200\times36=0\).
Since \(A(m)=7200 - 200m\) (\(m = 0,1,\cdots,36\)), \(A(m)\) takes values \(7200,7000,\cdots,0\). These are all multiples of 200 in the range from 0 to 7200.

Answer:

all multiples of 200 from 0 to 7,200