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| Section | Objectives |
|---|---|
| Functions and Algebra of Functions | - Derive conclusions based on data - Derive conclusions based on notation - Derive conclusions based on graphs |
| Polynomial Functions | - Interpret inputs and outputs for polynomial functions - Interpret concavity for polynomial functions - Interpret rates of change for polynomial functions |
| Graphical Depictions | - Interpret concavity for situations - Interpret asymptotes for situations - Interpret maximum and minimum for situations - Interpret inputs and outputs for situations - Interpret rates of change for situations |
| Logistic Functions | - Interpret inputs and outputs for logistic functions - Interpret asymptotes for logistic functions - Interpret rates of change for logistic functions |
| Exponential Functions | - Interpret inputs and outputs for exponential functions - Interpret rates of change for exponential functions - Interpret concavity for exponential functions |
| Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
| Validity of Models | - Examine utility - Determine fit - Determine validity |
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NEW QUESTION # 51
A vehicle is travelling away from a rest stop. The function
D(t)=48t+23
represents the distance from the vehicle to the rest stop at time t, where t is measured in hours and D is measured in miles.
What is the value of D(1.7)?
Answer: C
Explanation:
The function is:
D(t)=48t+23
This is a linear function because it has the form:
D(t)=mt+b
where:
48
is the rate of change, and:
23
is the starting distance from the rest stop.
We need to find:
D(1.7)
That means substitute:
t=1.7
into the function.
D(1.7)=48(1.7)+23
First multiply:
48(1.7)=81.6
Now add 23:
D(1.7)=81.6+23
D(1.7)=104.6
So the vehicle is:
104.6 miles
from the rest stop after 1.7 hours.
NEW QUESTION # 52
The graph shows the number of trees sold by a nursery, where the number of days since the beginning of the month is along the horizontal axis and the number of trees sold per day is along the vertical axis. The greatest number of trees are sold when the temperature is over 70°F.
When was the temperature likely over 70°F?
Answer: A
Explanation:
The problem states that the greatest number of trees are sold when the temperature is over 70°F. Therefore, we need to identify the days on the graph when tree sales are highest. The graph shows two major peaks in the number of trees sold per day. These peaks occur around day 2 and day 10. Since higher tree sales are linked to temperatures over 70°F, those two days are the most likely days when the temperature exceeded 70°F. Day 6 appears near a low point, so it is not likely associated with high temperature based on the given relationship.
Day 12 also does not match the main peaks. Therefore, the correct answer is C.
NEW QUESTION # 53
The data in the scatterplot represents the number of monthly train crossings at a particular intersection over time.
Which type of function should be used to model the data?
Answer: A
Explanation:
The scatterplot shows the number of monthly train crossings decreasing over time. The decrease is not constant from one year to the next, so a linear model is not the best choice. Instead, the data decreases quickly at first and then begins to level off, which is characteristic of exponential decay. Exponential models are appropriate when a quantity changes by a repeated factor or percentage over equal time intervals. A logistic model would usually show an S-shaped pattern with a carrying capacity, and a polynomial model would be more appropriate for turning points or more complex curvature. Since the points show a smooth decreasing curve that flattens over time, an exponential function best models the data. Therefore, the correct answer is B.
NEW QUESTION # 54
A researcher collected data on the number of large donations per year to a charitable organization. The results are shown in the scatterplot. A regression function is graphed with r
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