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 explains the function representing the total amount of property tax for a home based on the taxable value of x thousand dollars.
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
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and
use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three
investment?
STEP 1: The formula for compound interest is
A =
nt
= P(1 + − − ) n²,
where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to
A = Pert
Find r and n for each model, and use these values to write A in terms of t for each case.
Annual Model
r=0.10
A = Y(t) = 1150 (1.10)*
n = 1
Quarterly Model
r = 0.10
n = 4
A = Q(t) = 1150(1.025) 4t
Continuous Model
r=0.10
A = C(t) =…
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