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| Section | Objectives |
|---|---|
| Polynomial Functions | - Interpret rates of change for polynomial functions - Interpret concavity for polynomial functions - Interpret inputs and outputs for polynomial functions |
| Functions and Algebra of Functions | - Derive conclusions based on notation - Derive conclusions based on data - Derive conclusions based on graphs |
| Linear Functions | - Interpret rates of change for linear functions - Interpret inputs and outputs of linear functions |
| Graphical Depictions | - Interpret concavity for situations - Interpret inputs and outputs for situations - Interpret asymptotes for situations - Interpret rates of change for situations - Interpret maximum and minimum for situations |
| Validity of Models | - Determine fit - Examine utility - Determine validity |
| Exponential Functions | - Interpret rates of change for exponential functions - Interpret inputs and outputs for exponential functions - Interpret concavity for exponential functions |
| Logistic Functions | - Interpret asymptotes for logistic functions - Interpret rates of change for logistic functions - Interpret inputs and outputs for logistic functions |
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NEW QUESTION # 107
A new company just launched and is using the function M(t)to predict its market share after tyears. The graph of M(t)is shown.
When should the company expect to have a market share of 40%?
Answer: A
Explanation:
The function M(t)represents the company's market share after tyears.
The horizontal axis represents:
t= " time in years "
The vertical axis represents:
M(t)= " market share percentage "
We need to find when the market share reaches:
40%
From the graph, locate 40on the vertical axis. Then move horizontally to the blue curve and read the corresponding value on the horizontal axis.
The curve reaches 40%at approximately:
t=7.4
So the company should expect to have a market share of 40%after about:
7.4 " years "
Therefore, the correct answer is:
# ( " C " )
NEW QUESTION # 108
The graph shows the number of user accounts on a social media website over time.
When did the number of user accounts reach 4,500?
Answer: D
Explanation:
The graph represents the number of user accounts over time.
The horizontal axis represents:
" Time in months "
The vertical axis represents:
" Number of user accounts "
We need to find when the number of user accounts reached:
4,500
On the vertical axis, 4,500is halfway between:
3,000
and
6,000
So we look for the point where the blue curve reaches that height.
From the graph, the curve reaches approximately 4,500user accounts at:
x#2.0
That means the website had about 4,500user accounts after approximately:
2.0 " months "
NEW QUESTION # 109
The value of a collectible coin can be modeled by F(t), where t represents years since the number of years since the coin was found, and the vertical axis represents the value, in thousands of dollars.
How is the value of the coin changing over time based on the graph?
Answer: C
Explanation:
The graph shows the value of the coin increasing over time. Since the curve rises from left to right, the value is not decreasing. The graph also becomes steeper as time increases, which means the rate of increase is getting larger. In Applied Algebra, when a graph is increasing and its slope is increasing, the quantity is described as increasing faster and faster. This is typical of exponential growth, where values grow by a repeated percent or factor rather than by a constant amount. The choices involving decreasing are incorrect because the graph moves upward. The choice "increasing slower and slower" would require the graph to flatten, which it does not. Therefore, the correct answer is B.
NEW QUESTION # 110
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 # 111
The function F(n) represents the relationship between the number of animals in two enclosures, where n is the number of animals in enclosure A and F is the number of animals in enclosure B. The number of animals in enclosure B is 20 more than the number of animals in enclosure A.
Which function represents this situation?
Answer: A
Explanation:
The function F(n) gives the number of animals in enclosure B.
The input n represents the number of animals in enclosure A.
The problem says enclosure B has 20 more animals than enclosure A. The phrase "20 more than" means we add 20:
F(n)=n+20
For example, if enclosure A had 30 animals, then enclosure B would have:
F(30)=30+20=50
So the function that represents the situation is:
F(n)=n+20
NEW QUESTION # 112
......
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