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| Section | Objectives |
|---|---|
| Topic 1: Logistic Functions | - Interpret asymptotes for logistic functions - Interpret inputs and outputs for logistic functions - Interpret rates of change for logistic functions |
| Topic 2: Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
| Topic 3: Validity of Models | - Determine fit - Examine utility - Determine validity |
| Topic 4: Polynomial Functions | - Interpret concavity for polynomial functions - Interpret rates of change for polynomial functions - Interpret inputs and outputs for polynomial functions |
| Topic 5: Exponential Functions | - Interpret concavity for exponential functions - Interpret rates of change for exponential functions - Interpret inputs and outputs for exponential functions |
| Topic 6: Graphical Depictions | - Interpret asymptotes for situations - Interpret maximum and minimum for situations - Interpret concavity for situations - Interpret inputs and outputs for situations - Interpret rates of change for situations |
| Topic 7: Functions and Algebra of Functions | - Derive conclusions based on notation - Derive conclusions based on data - Derive conclusions based on graphs |
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NEW QUESTION # 90
A researcher collected data on the average selling price for tickets to a concert over time. The results are shown in the scatterplot. A regression function is graphed with r
2=0.56. The predicted average selling price for tickets after 10.8 days is $167.20.
Is this prediction appropriate?
Answer: B
Explanation:
The regression model has r2=0.56, which indicates a moderate fit. A moderate fit is not as reliable as a strong fit, but it can still be used for limited prediction when the extrapolation is close to the observed data. The prediction is made at x=10.8 days. This value is slightly beyond the maximum observed x-value, so the prediction is an extrapolation. For a moderate fit, the x-value should remain within about 25% of the range beyond the maximum value. In this case, x=10.8 is within that acceptable range, so the prediction is appropriate. Therefore, the correct answer is B.
NEW QUESTION # 91
The population of fish in a lake is changing according to the function
P(t)=24t+185
where tis 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 is:
P(t)=24t+185
This is a linear function in the form:
P(t)=mt+b
where:
m= " rate of change "
and
b= " initial value "
In the function:
P(t)=24t+185
the coefficient of tis:
24
So the rate of change is:
24 " fish per month "
Because 24is positive, the fish population is increasing.
The number 185is not the rate of change. It represents the starting fish population at the beginning of the year, when t=0:
P(0)=24(0)+185=185
Therefore, the correct interpretation is:
" The number of fish in the lake is increasing at a constant rate of 24 fish per month. " So the correct answer is:
# ( " B " )
NEW QUESTION # 92
A cart is being loaded with boxes, and each box has the same weight. After 4 boxes are loaded, the total weight of the boxes and cart is 116 pounds. After 9 boxes are loaded, the total weight is 161 pounds.
What is the weight of each box?
Answer: A
Explanation:
This situation can be modeled with a linear relationship because each box has the same weight.
We are given:
4 " boxes " #116 " pounds "
and
9 " boxes " #161 " pounds "
The weight increases because more boxes are added.
First, find the change in total weight:
161-116=45
Then find the change in the number of boxes:
9-4=5
Since 5 additional boxes increased the total weight by 45 pounds, the weight of each box is:
45/5=9
So each box weighs:
9 " pounds "
Check:
If each box weighs 9 pounds, then adding 5 more boxes adds:
5(9)=45
116+45=161
This matches the given information.
NEW QUESTION # 93
The scatterplot shows data on the usage of a computer ' s CPU over time. The graphed regression function has an r