# A couple seeking to buy a home

A couple seeking to buy a home decides that a monthly payment of \$1600 fits their budget. The amount they can borrow, A, is a function of the time t, in years, it will take to repay the debt. If we denote this function by

A = f(t),

then the following table defines the function.

t A t A
5 80,000 20 199,000
10 135,000 25 217,000
15 173,000 30 229,000
(a) Find f(20).

f(20) =

Write a sentence that explains its meaning.

It will take this number of years to pay off a debt of 20 thousand dollars.The couple must repay this much per year for every \$20 borrowed.     The couple can reduce their payments by \$20 if they reduce the amount they borrow by this much.It will take 20 years to pay off a debt of this amount.

(b) Does

f(5 + 5) = f(5) + f(5)?

Explain.

Yes, because f(5 + 5) = f(10) and f(5) + f(5) = f(10).Yes, because f(5 + 5) = f(25) and f(5) + f(5) = f(25).     No, because f(5 + 5) = f(10) which is not equal to f(5) + f(5).No, because f(5) + f(5) = f(25) which is not equal to f(5 + 5).

(c) If the couple is looking at a house that requires them to finance \$173,000, how long must they make payments? Write this correspondence in the form

A = f(t),

where t is measured in years.

\$173,000 = f

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