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Jeff Koegel

Lebanon Valley College
Teacher of Mathematics

Biography

I just completed my 25th year teaching high school mathematics. I have been teaching AP Calculus AB and AP Calculus BC for the past 21 years. I also work as an AP Reader for ETS grading free-response questions from the AP Calculus exams. I also currently teach Math Analysis and have also taught Algebra 1, Algebra 2, and various Pre-Calculus courses. I am a Google Certified Educator (Level 1 and Level 2) and also hold Level 1 & Level 2 Kami certification. I was named Educator of the Year at my high school this past school year. I hold a B.S. in mathematics (summa cum laude) and two master's degrees (one in curriculum & instruction and the other in educational administration), each with a 4.0 GPA.

Education

BS Mathematics
Lebanon Valley College
MS Curriculum & Instruction
University of Scranton
MS Educational Administration
Purdue University Northwest

Educator Statistics

Numerade tutor for 5 years
3 Students Helped

Topics Covered

Mastering the Basics of Parametric Equations: A Comprehensive Guide
Polar Coordinates: Understanding the Basics and Applications
Master Trigonometry with Our Comprehensive Guide
Mastering Vectors: An Introduction to Vector Basics
Understanding Complex Numbers: A Comprehensive Guide
Functions
Mastering Polynomials: Essential Tips and Tricks | [Brand Name]
Rational Functions: Understanding Their Properties and Applications

Jeff's Textbook Answer Videos

03:08
Precalculus

Tax Revenue Economist Arthur Laffer has been a center of controversy because of his Laffer curve, an idealized version of which is shown here.
According to this curve, increasing a tax rate, say from $x_{1}$ percent to $x_{2}$ percent on the graph, can actually lead to a decrease in government revenue. All economists agree on the endpoints, 0 revenue at tax rates of both $0 \%$ and $100 \%,$ but there is much disagreement on the location of the rate $x_{1}$ that produces maximum revenue. Suppose an economist studying the Laffer curve produces the rational function
$$
R(x)=\frac{80 x-8000}{x-110}
$$
where $R(x)$ is government revenue in tens of millions of dollars for a tax rate of $x$ percent, with the function valid for $55 \leq x \leq 100$. Find the revenue for the following tax rates. Round to the nearest tenth if necessary.
(a) $55 \%$
(b) $60 \%$
(c) $70 \%$
(d) $90 \%$
(e) $100 \%$
(GRAPH CANT COPY)

Chapter 3: Polynomial and Rational Functions
Section 5: Rational Functions: Graphs, Applications, and Models
Jeff Koegel
03:03
Precalculus

Tax Revenue See Exercise 117 . Suppose an economist determines that
$R(x)=\frac{60 x-6000}{x-120}$
where $y=R(x)$ is government revenue in tens of millions of dollars for a tax rate of $x$ percent, with $y=R(x)$ valid for $50 \leq x \leq 100 .$ Find the revenue for each tax rate. Round to the nearest tenth if necessary.
(a) $50 \%$
(b) $60 \%$
(c) $80 \%$
(d) $100 \%$

Chapter 3: Polynomial and Rational Functions
Section 5: Rational Functions: Graphs, Applications, and Models
Jeff Koegel
1

Jeff's Quick Ask Videos

02:17
Calculus 1 / AB

Suppose that 2400 dollars is deposited into a savings account earning an interest rate of 5% compounded monthly.
Find a formula for A(t), the account balance after t years.
A(t)=
What is the account balance after 3 years?
Balance =
dollars

1