The millage rate is the amount of property tax per $1000 of the taxable value of a home. For a certain county the millage rate is 24 mil ($24 in tax per $1000 of taxable value of the home). A city within the county also imposes a flat fee of $108 per home. a. Write a function representing the total amount of property tax T ( x ) ( in $ ) for a home with a taxable value of x thousand dollars. b. Write an equation for T − 1 ( x ) . c. What does the inverse function represent in the context of this problem? d. Evaluate T − 1 ( 2988 ) and interpret its meaning in context.
The millage rate is the amount of property tax per $1000 of the taxable value of a home. For a certain county the millage rate is 24 mil ($24 in tax per $1000 of taxable value of the home). A city within the county also imposes a flat fee of $108 per home. a. Write a function representing the total amount of property tax T ( x ) ( in $ ) for a home with a taxable value of x thousand dollars. b. Write an equation for T − 1 ( x ) . c. What does the inverse function represent in the context of this problem? d. Evaluate T − 1 ( 2988 ) and interpret its meaning in context.
Solution Summary: The author calculates the inverse of an equation for T-1(x).
The millage rate is the amount of property tax per $1000 of the taxable value of a home. For a certain county the millage rate is 24 mil ($24 in tax per $1000 of taxable value of the home). A city within the county also imposes a flat fee of $108 per home.
a. Write a function representing the total amount of property tax
T
(
x
)
(
in $
)
for a home with a taxable value of x thousand dollars.
b. Write an equation for
T
−
1
(
x
)
.
c. What does the inverse function represent in the context of this problem?
d. Evaluate
T
−
1
(
2988
)
and interpret its meaning in context.
A rectangular box is to have a square base and a volume of 30 ft3. The material for the base costs 34¢/ft2, the material for the sides costs 10¢/ft2, and the material for the top costs 25¢/ft2. Letting x denote the length of one side of the base, find a function in the variable x giving the cost (in dollars) of constructing the box.
A rectangular box is shown. The base of the box has length and width each labeled x. The height of the box is labeled y.
f(x) =
Express the give quantity in terms of the indicated variable.
The interest obtained after one year on an investment at 2 1/2% simple interest per year; x = number of dollars invested.
Use function notation to represent $1700 more than a faculty member's salary after 6 years on the job.
Use function notation to represent a salary that is 3 times as large as the salary of a faculty member after 7 years on the job.
How many times as large is the salary of a faculty member who has been on the job for 14 years as compared to someone who has been on the job for 3.2 years?
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