Millage rate is the amount per $1000 that is often used to calculate property tax. For example, a home with a $ 60 , 000 taxable value in a municipality with a 19 mil tax rate would require 0 .019 $60,000 =$1140 in property taxes. In one county, homeowners pay a flat tax of $172 plus a rate of 19 mil on the taxable value of a home. a. Write a linear function that represents the total property tax T x for a home with a taxable value of x dollars. b. Evaluate T 80 , 000 and interpret the meaning in the context of this problem.
Millage rate is the amount per $1000 that is often used to calculate property tax. For example, a home with a $ 60 , 000 taxable value in a municipality with a 19 mil tax rate would require 0 .019 $60,000 =$1140 in property taxes. In one county, homeowners pay a flat tax of $172 plus a rate of 19 mil on the taxable value of a home. a. Write a linear function that represents the total property tax T x for a home with a taxable value of x dollars. b. Evaluate T 80 , 000 and interpret the meaning in the context of this problem.
Millage rate is the amount per
$1000
that is often used to calculate property tax. For example, a home with a
$
60
,
000
taxable value in a municipality with a 19 mil tax rate would require
0
.019
$60,000
=$1140
in property taxes. In one county, homeowners pay a flat tax of
$172
plus a rate of 19 mil on the taxable value of a home.
a. Write a linear function that represents the total property tax
T
x
for a home with a taxable value of
x
dollars.
b. Evaluate
T
80
,
000
and interpret the meaning in the context of this problem.
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) =…
College Algebra with Modeling & Visualization (5th Edition)
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