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| Section | Objectives |
|---|---|
| Validity of Models | - Examine utility - Determine validity - Determine fit |
| Logistic Functions | - Interpret rates of change for logistic functions - Interpret inputs and outputs for logistic functions - Interpret asymptotes for logistic functions |
| Exponential Functions | - Interpret rates of change for exponential functions - Interpret inputs and outputs for exponential functions - Interpret concavity for exponential functions |
| Functions and Algebra of Functions | - Derive conclusions based on graphs - Derive conclusions based on data - Derive conclusions based on notation |
| Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
| Graphical Depictions | - Interpret inputs and outputs for situations - Interpret rates of change for situations - Interpret asymptotes for situations - Interpret concavity for situations - Interpret maximum and minimum for situations |
| Polynomial Functions | - Interpret concavity for polynomial functions - Interpret rates of change for polynomial functions - Interpret inputs and outputs for polynomial functions |
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NEW QUESTION # 28
The function d(x)=14+65xrepresents the distance, in meters, from a tower to an object at time x, in seconds.
What is the value of d(1.5)?
Answer: D
Explanation:
We are given the function:
d(x)=14+65x
This is a linear function because it has the form:
d(x)=mx+b
where 65is the rate of change and 14is the starting value.
We need to find:
d(1.5)
That means substitute x=1.5into the function:
d(1.5)=14+65(1.5)
Now multiply:
65(1.5)=97.5
Then add:
d(1.5)=14+97.5
d(1.5)=111.5
So the distance from the tower to the object at 1.5seconds is:
111.5 " meters "
NEW QUESTION # 29
The function p(t)represents the number of active players, p, in a game thours after 11:00 a.m. The graph of p(t) is shown.
What is one example of an interval for which the number of players is decreasing faster and faster?
Answer: D
Explanation:
The graph represents:
p(t)= " number of active players "
where:
t= " hours after 11:00 a.m. "
The phrase "decreasing faster and faster" means two things are happening:
The graph is going downward, so the number of players is decreasing.
The graph is becoming steeper downward, so the rate of decrease is increasing.
This corresponds to a graph that is decreasing and concave down.
Looking at the graph, the number of active players reaches a maximum around:
t#9
After that, the graph begins decreasing. Near the far right side of the graph, especially around:
t=11.2 " to " t=11.5
the curve is dropping more and more steeply.
That means the number of players is decreasing faster and faster on that interval.
NEW QUESTION # 30
The number of acres affected by an invasive species can be modeled using the logistic function f(x), where xrepresents the number of months since the species was introduced and f(x)represents the number of affected acres. The graph of f(x)is shown.
What happens as time progresses from month 2 to month 6?
Answer: D
Explanation:
This is also a logistic growth curve.
Analyze the interval from month 2 to month 6:
The graph is increasing during this time.
The curve is becoming steeper, meaning the slope is increasing.
This indicates the rate of change is getting larger over time.
So, the number of affected acres is:
" increasing faster and faster "
This corresponds to the early-to-middle growth phase of a logistic function.
NEW QUESTION # 31
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: D
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 # 32
The function a(x)represents the value of an investment account, where xis the number of years since the account was opened. The graph of the function is shown.
What is the total value when x=4?
Answer: A
Explanation:
The function a(x)represents the total value of an investment account.
The horizontal axis represents:
x= " time in years "
The vertical axis represents:
a(x)= " total account value in dollars "
We are asked to find the total value when:
x=4
To answer this from the graph:
Locate x=4on the horizontal axis.
Move vertically upward until reaching the blue graph.
Read the corresponding value on the vertical axis.
From the graph, when x=4, the value is slightly above $1,800, approximately:
a(4)#1,830.59
So the total value of the investment account after 4 years is approximately:
$1,830.59
NEW QUESTION # 33
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