example 4 loan repayment chapter 4.3 a business property is purchased with a promise to pay off a...
TRANSCRIPT
example 4 Loan Repayment
Chapter 4.3
A business property is purchased with a promise to pay off a $60,000 loan plus the$16,500 interest on this loan by making 60 monthly payments of $1275. The amount ofmoney remaining to be paid on the loan plus interest is given by the function
where x is the number of months remaining for payments to be made.
( ) 76,500 1275f x x
a. Find the inverse of this function.
b. Use the inverse to determine how many months remain to make payments if $35,700 remains to be paid.
2009 PBLPathways
2009 PBLPathways
A business property is purchased with a promise to pay off a $60,000 loan plus the$16,500 interest on this loan by making 60 monthly payments of $1275. The amount ofmoney remaining to be paid on the loan plus interest is given by the function
where x is the number of months remaining for payments to be made.
( ) 76,500 1275f x x
a. Find the inverse of this function.
b. Use the inverse to determine how many months remain to make payments if $35,700 remains to be paid.
2009 PBLPathways
( ) 76,500 1275f x x
a. Find the inverse of this function.
Number of months remaining to be paid
Amount of money remaining to be paid
1
76,500 1275
76,500 1275
76,500 1275
76,500
1275
76,500
1275
76,500( )
1275
y x
x y
x y
xy
xy
xf x
Replace f(x) with y
Interchange x and y
Solve for y
Replace y with f -1(x)
2009 PBLPathways
( ) 76,500 1275f x x
a. Find the inverse of this function.
Number of months remaining to be paid
Amount of money remaining to be paid
1
76,500 1275
76,500 1275
76,500 1275
76,500
1275
76,500
1275
76,500( )
1275
y x
x y
x y
xy
xy
xf x
Replace f(x) with y
Interchange x and y
Solve for y
Replace y with f -1(x)
2009 PBLPathways
( ) 76,500 1275f x x
a. Find the inverse of this function.
Number of months remaining to be paid
Amount of money remaining to be paid
1
76,500 1275
76,500 1275
76,500 1275
76,500
1275
76,500
1275
76,500( )
1275
y x
x y
x y
xy
xy
xf x
Replace f(x) with y
Interchange x and y
Solve for y
Replace y with f -1(x)
2009 PBLPathways
( ) 76,500 1275f x x
a. Find the inverse of this function.
Number of months remaining to be paid
Amount of money remaining to be paid
1
76,500 1275
76,500 1275
76,500 1275
76,500
1275
76,500
1275
76,500( )
1275
y x
x y
x y
xy
xy
xf x
Replace f(x) with y
Interchange x and y
Solve for y
Replace y with f -1(x)
2009 PBLPathways
( ) 76,500 1275f x x
a. Find the inverse of this function.
Number of months remaining to be paid
Amount of money remaining to be paid
1
76,500 1275
76,500 1275
76,500 1275
76,500
1275
76,500
1275
76,500( )
1275
y x
x y
x y
xy
xy
xf x
Replace f(x) with y
Interchange x and y
Solve for y
Replace y with f -1(x)
2009 PBLPathways
( ) 76,500 1275f x x
a. Find the inverse of this function.
Number of months remaining to be paid
Amount of money remaining to be paid
1
76,500 1275
76,500 1275
76,500 1275
76,500
1275
76,500
1275
76,500( )
1275
y x
x y
x y
xy
xy
xf x
Replace f(x) with y
Interchange x and y
Solve for y
Replace y with f -1(x)
2009 PBLPathways
( ) 76,500 1275f x x
a. Find the inverse of this function.
Number of months remaining to be paid
Amount of money remaining to be paid
1
76,500 1275
76,500 1275
76,500 1275
76,500
1275
76,500
1275
76,500( )
1275
y x
x y
x y
xy
xy
xf x
Replace f(x) with y
Interchange x and y
Solve for y
Replace y with f -1(x)
2009 PBLPathways
( ) 76,500 1275f x x
b. Use the inverse to determine how many months remain to make payments if $35,700 remains to be paid.
Number of months remaining to be paid
Amount of money remaining to be paid
1 76,500( )
1275
xf x
Amount of money remaining to be paid
Number of months remaining to be paid
1 76,500 35,700(35,700) 32
1275f
2009 PBLPathways
( ) 76,500 1275f x x
b. Use the inverse to determine how many months remain to make payments if $35,700 remains to be paid.
Number of months remaining to be paid
Amount of money remaining to be paid
1 76,500( )
1275
xf x
Amount of money remaining to be paid
Number of months remaining to be paid
1 76,500 35,700(35,700) 32
1275f
2009 PBLPathways
( ) 76,500 1275f x x
b. Use the inverse to determine how many months remain to make payments if $35,700 remains to be paid.
Number of months remaining to be paid
Amount of money remaining to be paid
1 76,500( )
1275
xf x
Amount of money remaining to be paid
Number of months remaining to be paid
1 76,500 35,700(35,700) 32
1275f