Mortgage A couple can afford $800 per month to purchase a home. As indicated in the table, if they can get an interest rate of 7.5%, the number of years t that it will take to pay off the mortgage is a function of the dollar amount A of the mortgage for the home they purchase.
Amount A ($) | t(years) |
40,000 | 5 |
69,000 | 10 |
89,000 | 15 |
103,000 | 20 |
120,000 | 30 |
(Source: Comprehensive Mortgage Tables [Publication No. 492], Financial Publishing Co.)
a. If the couple wishes to finance $103,000, for how long must they make payments? Write this correspondence in function form if t = f(A).
b. What is f (120,000)? Write a sentence that explains its meaning.
c. What is f (3 · 40,000)?
d. What value of A makes f(A) = 5 true?
e. Does f(3 · 40,000) = 3 · f(40,000)? Explain your reasoning.
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