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| Section | Weight | Objectives |
|---|---|---|
| Linear Equations and Inequalities | 25% | - Solving single-variable equations - Solving and graphing inequalities - Real-world applications |
| Algebraic Expressions and Operations | 20% | - Simplifying and evaluating expressions - Variables, constants, and coefficients - Order of operations - Operations with polynomials |
| Systems of Equations and Inequalities | 15% | - Graphical solutions - Applications of systems - Solving by substitution and elimination |
| Graphing and Functions | 25% | - Slope and equations of lines - Function notation and evaluation - Coordinate plane and plotting points - Linear functions and their graphs |
| Exponents, Radicals, and Quadratic Relationships | 15% | - Properties of exponents - Basic quadratic graphs - Simplifying radical expressions - Solving quadratic equations |
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NEW QUESTION # 99
Based on collected data, the value of a painting can be modeled using the exponential function f(x)=240(1.12) x
. In this case, x represents the number of years since 2005, and f(x) represents the value of the painting in dollars.
Which value represents the average yearly rate of change of the painting's value from 2013 to 2015?
Answer: B
Explanation:
This problem asks for an average yearly rate of change over a time interval. Since x represents years since
2005, the year 2013 corresponds to x=8, and the year 2015 corresponds to x=10. Use the average rate of change formula:
10#8
f(10)#f(8)
Evaluating the model gives f(8)=240(1.12)
8
#594.23 and f(10)=240(1.12)
10
#745.40. The total change is approximately 151.17 dollars over 2 years. Dividing by 2 gives about 75.59 dollars per year. Since the question asks for the average yearly rate, not the total increase, the correct answer is B.
NEW QUESTION # 100
The function P(t)represents the daily profit, in hundreds of dollars, for a hardware store since opening. The graph of P(t)is shown.
How should the maximum value be interpreted?
Answer: B
Explanation:
The graph shows P(t), where:
t= " years since opening "
and
P(t)= " daily profit in hundreds of dollars "
The graph is a downward-opening curve, so its maximum value occurs at the highest point of the graph, also called the vertex.
From the graph, the highest point occurs at approximately:
t=9
So the maximum daily profit happened approximately:
9 " years after opening "
The vertical value at this maximum point is approximately:
P(t)=29
But the graph measures profit in hundreds of dollars, so:
29×100=2900
Therefore, the maximum daily profit was approximately:
$2,900
So the correct interpretation is:
" Approximately 9 years after opening, a maximum daily profit of approximately " $2,900 " was earned. "
NEW QUESTION # 101
An exponential growth function can be used to model the number of bacteria in a population. The function G(t)=1,600× # 1.31 #
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