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.
Consider the function f(x) = x²-1.
(a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative.
Show all your steps clearly.
(b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the
graph where x 1 and x->
1+h (for a small positive value of h, illustrate conceptually). Then,
draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the
value you found in part (a).
(c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in
the context of the graph of f(x). How does the rate of change of this function vary at different
points?
1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist,
state that fact.
и
(a) f'(-5)
(b) f'(-3)
(c) f'(0)
(d) f'(5)
2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5)
=
4.
-
3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2)
and f'(2).
College Algebra with Modeling & Visualization (5th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Discrete Distributions: Binomial, Poisson and Hypergeometric | Statistics for Data Science; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=lHhyy4JMigg;License: Standard Youtube License