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| Section | Objectives |
|---|---|
| Validity of Models | - Determine fit - Determine validity - Examine utility |
| Graphical Depictions | - Interpret maximum and minimum for situations - Interpret inputs and outputs for situations - Interpret rates of change for situations - Interpret asymptotes for situations - Interpret concavity for situations |
| Polynomial Functions | - Interpret concavity for polynomial functions - Interpret inputs and outputs for polynomial functions - Interpret rates of change for polynomial functions |
| Functions and Algebra of Functions | - Derive conclusions based on graphs - Derive conclusions based on notation - Derive conclusions based on data |
| Exponential Functions | - Interpret rates of change for exponential functions - Interpret inputs and outputs for exponential functions - Interpret concavity for exponential functions |
| Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
| Logistic Functions | - Interpret asymptotes for logistic functions - Interpret rates of change for logistic functions - Interpret inputs and outputs for logistic functions |
1. A researcher collected data on the number of annual bear sightings in a region over time. The results are shown in the scatterplot. The graphed regression function has an r
2value of 0.41. The predicted number of annual bear sightings after 19.4 years is 88.5.
Is this prediction appropriate?
A) Yes. The r2value indicates a strong fit, and x=19.4 is within 50% of the range of the maximum value.
B) No. The r2value indicates a moderate fit, but x=19.4 is more than 25% of the range beyond the maximum value.
C) No. The r2value indicates a strong fit, but x=19.4 is more than 50% of the range beyond the maximum value.
D) Yes. The r2value indicates a moderate fit, and x=19.4 is within 25% of the range of the maximum value.
2. The function P(t)represents the daily profit, in hundreds of dollars, for a hardware store since opening. The graph of P(t)is shown.
How should the maximum value be interpreted?
A) Approximately 21 years after opening, a maximum daily profit of approximately $1,270was earned.
B) Approximately 9 years after opening, a maximum daily profit of approximately $1,270was earned.
C) Approximately 9 years after opening, a maximum daily profit of approximately $2,900was earned.
D) Approximately 21 years after opening, a maximum daily profit of approximately $2,900was earned.
3. 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?
A) 1,000
B) 4,500
C) 25
D) 2,250
4. Consider the graph of h(t) shown. The function represents the height, h, in feet, of a ball t seconds after being launched.
What is the point, if any, at which the concavity changes from concave down to concave up?
A) At t=0.705
B) The graph is always concave up.
C) At t=1.41
D) The graph is always concave down.
5. The graph shows the number of people at an event venue after 3:00 p.m., in thousands.
Which rate of change is the greatest?
A) The average rate of change from point A to point C
B) The instantaneous rate of change at point C
C) The instantaneous rate of change at point D
D) The average rate of change from point C to point D
Solutions:
| Question # 1 Answer: B | Question # 2 Answer: C | Question # 3 Answer: A | Question # 4 Answer: D | Question # 5 Answer: B |
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