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| Section | Objectives |
|---|---|
| Exponential Functions | - Interpret inputs and outputs for exponential functions - Interpret concavity for exponential functions - Interpret rates of change for exponential functions |
| Logistic Functions | - Interpret rates of change for logistic functions - Interpret asymptotes for logistic functions - Interpret inputs and outputs for logistic functions |
| Graphical Depictions | - Interpret rates of change for situations - Interpret concavity for situations - Interpret asymptotes for situations - Interpret maximum and minimum for situations - Interpret inputs and outputs for situations |
| Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
| Functions and Algebra of Functions | - Derive conclusions based on data - Derive conclusions based on notation - Derive conclusions based on graphs |
| Validity of Models | - Determine fit - Determine validity - Examine utility |
| Polynomial Functions | - Interpret inputs and outputs for polynomial functions - Interpret rates of change for polynomial functions - Interpret concavity for polynomial functions |
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NEW QUESTION # 116
The number of letters processed daily at a mail center is modeled by the decreasing exponential function shown in the graph.
What is the long-term trend in the number of letters processed per day, based on the equation of the horizontal asymptote?
Answer: B
Explanation:
In an exponential decay model, the horizontal asymptote represents the long-term value that the function approaches as time increases. The graph shows the number of letters processed per day decreasing quickly at first and then leveling off. Since the graph approaches the horizontal line y=1000, the long-term trend is 1,000 letters per day. This does not mean the mail center immediately processes exactly 1,000 letters, but it means the model predicts the daily number will get closer and closer to 1,000 over time. The other choices either represent values too low or values from earlier parts of the graph, not the asymptote. Therefore, the correct answer is B.
NEW QUESTION # 117
The number of property sales in a region this year is expected to be 3 times the number of property sales in the region last year. The function H(x) represents the number of property sales this year, where x represents the number of properties sold last year. Which notation represents the number of property sales this year, given that the number of properties sold last year was 280?
Answer: D
Explanation:
This problem uses function notation to describe a multiplicative relationship. The input x is the number of properties sold last year, and the output H(x) is the expected number sold this year. Since this year's sales are
3 times last year's sales, the function rule is H(x)=3x. The given input is 280 because 280 properties were sold last year. Substituting gives H(280)=3(280)=840. That means 840 property sales are expected this year. The answer choice must show the correct input of 280 and the correct output of 840. The other options either reverse the values or use an incorrect output. Therefore, the correct answer is C.
NEW QUESTION # 118
The number of new user accounts per day on a website is modeled by a decreasing exponential function. The graph of the function is shown.
Which statement is justified considering the location of the horizontal asymptote?
Answer: D
Explanation:
The graph shows a decreasing exponential function.
The horizontal axis represents:
" Time in months "
The vertical axis represents:
" New user accounts per day "
The graph starts near 7,000new user accounts per day and decreases over time. However, it does not decrease toward 0. Instead, the graph levels off near a horizontal value around:
y=2,500
This horizontal value is the horizontal asymptote.
A horizontal asymptote shows the long-term value the function approaches. Since the asymptote is above 0, the model predicts that the number of daily new user accounts approaches a positive value, not zero.
So the justified statement is:
" The number of daily new user accounts will not decrease to 0. "
NEW QUESTION # 119
The number of members of a religious organization can be modeled using the logistic function f(x), where xrepresents the number of years since the organization was started and f(x)represents the number of members.
The graph of f(x)is shown.
What is one range of values for which the graph is concave down?
Answer: C
Explanation:
The graph is a logistic growth curve.
A logistic growth curve has two main concavity regions:
" concave up before the inflection point "
and
" concave down after the inflection point "
From the graph, the function increases faster and faster until about:
x=6
After x=6, the graph continues increasing, but it begins to flatten out. That means the number of members is increasing slower and slower.
This is concave down behavior.
Therefore, one interval where the graph is concave down is:
(6#11)
So the correct answer is:
# ( " D " )
NEW QUESTION # 120
As sacks are unloaded off a wagon, the total weight of the wagon and sacks changes. Each sack has the same weight. After 5 sacks are removed, the total weight of the wagon and remaining sacks is 135 pounds. After 9 sacks are removed, the total weight is 87 pounds. What is the weight of each sack?
Answer: A
Explanation:
This situation has a constant rate of change because each sack weighs the same amount. After 5 sacks are removed, the total weight is 135 pounds. After 9 sacks are removed, the total weight is 87 pounds. From 5 to
9 sacks removed is 4 more sacks. Over the same interval, the total weight decreases by 135#87=48 pounds.
Since 4 sacks account for a 48-pound decrease, each sack must weigh 48÷4=12 pounds. This uses the linear idea that equal changes in the input produce equal changes in the output. Therefore, the weight of each sack is
12 pounds, which is answer A.
NEW QUESTION # 121
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