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| Section | Objectives |
|---|---|
| Foundations of Algebra | - Algebraic Expressions
|
| Linear Functions and Systems | - Linear Equations
|
| Polynomial and Rational Expressions | - Rational Expressions
|
| Exponential and Logarithmic Concepts | - Logarithmic Basics
|
| Functions and Graphs | - Function Concepts
|
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NEW QUESTION # 73
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 # 74
The function f(n) represents the relationship between the distances traveled by two vehicles, where n is the distance traveled by vehicle A and f is the distance traveled by vehicle B. The distance traveled by vehicle B is 17 more than the distance traveled by vehicle A.
Which function represents this situation?
Answer: C
NEW QUESTION # 75
The population of bison in a preserve can be modeled using the logistic function f(x), where x represents the number of years since the preserve was established and f(x) represents the population. The graph of f(x) is shown.
How does the bison population change as time progresses from year 7 to year 10?
Answer: D
Explanation:
A logistic function often increases quickly in the middle and then begins to level off as it approaches a maximum carrying capacity. From year 7 to year 10, the graph is still increasing, so the bison population is going up. However, the curve is becoming flatter during this interval. A flatter curve means the slope is getting smaller, so the population is increasing at a slower rate. This behavior is described as "increases slower and slower." It is not decreasing, because the graph continues to move upward. It is also not increasing faster and faster, because the slope is not becoming steeper in this interval. Therefore, the correct interpretation is answer B.
NEW QUESTION # 76
The function f(z) represents the relationship between the number of units in two inventories, where z is the number of units in inventory A and f(z) is the number of units in inventory B. The number of units in inventory B is 2 more than the number of units in inventory A. Which function represents this situation?
Answer: D
Explanation:
This problem translates a verbal statement into function notation. The variable z represents the number of units in inventory A, and f(z) represents the number of units in inventory B. The phrase "2 more than" tells us to add 2 to the number of units in inventory A. That gives the rule f(z)=z+2. For example, if inventory A has
10 units, then inventory B has f(10)=12 units. Option A subtracts 2, option C multiplies by 2, and option D divides by 2, so those do not match the stated relationship. Because inventory B is always exactly 2 more than inventory A, the correct function is f(z)=z+2. Therefore, the answer is B.
NEW QUESTION # 77
The population of fish in a lake is changing according to the function P(t)=31t+438, where t is the number of months since the beginning of the year and P(t) is the fish population at time t. Which interpretation of the rate of change is correct?
Answer: B
Explanation:
The function P(t)=31t+438 is linear and follows the form P(t)=mt+b. In this form, m is the rate of change and b is the initial value. Here, the coefficient of t is 31, so the fish population changes by 31 fish per month.
Because 31 is positive, the population is increasing rather than decreasing. The number 438 is the initial fish population at the start of the year, not the rate of change. Therefore, the correct interpretation is that the number of fish in the lake is increasing at a constant rate of 31 fish per month. That matches option A.
NEW QUESTION # 78
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