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| Section | Objectives |
|---|---|
| Validity of Models | - Determine fit - Examine utility - Determine validity |
| Exponential Functions | - Interpret inputs and outputs for exponential functions - Interpret rates of change for exponential functions - Interpret concavity for exponential functions |
| Logistic Functions | - Interpret inputs and outputs for logistic functions - Interpret rates of change for logistic functions - Interpret asymptotes for logistic functions |
| Functions and Algebra of Functions | - Derive conclusions based on data - Derive conclusions based on notation - Derive conclusions based on graphs |
| Graphical Depictions | - Interpret asymptotes for situations - Interpret concavity for situations - Interpret inputs and outputs for situations - Interpret rates of change for situations - Interpret maximum and minimum for situations |
| Linear Functions | - Interpret rates of change for linear functions - Interpret inputs and outputs of linear functions |
| 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 # 43
The function P(t) represents the yearly profit, in thousands of dollars, for a virtual store since opening. The graph of P(t) is shown.
What is the time at which the store reached the maximum yearly profit?
Answer: A
Explanation:
The maximum value of a graph is the highest output value the function reaches. Since P(t) represents yearly profit, the maximum value occurs where the store earns its greatest yearly profit. The graph is a downward- opening curve, so its highest point is the vertex. To answer the question, we need the t-value of the vertex, not the profit amount. From the graph, the highest point occurs between 4 and 5 years after opening, closest to 4.5 years. This means the virtual store reached its maximum yearly profit approximately 4.5 years after it opened.
The later values decrease after the vertex, so options involving 7.5 or 14 years are not correct. Therefore, the correct answer is B.
NEW QUESTION # 44
The number of property sales in a region this year is expected to be 3 times the number of property sales in the region last year. The function H(x) represents the number of property sales this year, where x represents the number of properties sold last year. Which notation represents the number of property sales this year, given that the number of properties sold last year was 280?
Answer: B
Explanation:
This problem uses function notation to describe a multiplicative relationship. The input x is the number of properties sold last year, and the output H(x) is the expected number sold this year. Since this year's sales are
3 times last year's sales, the function rule is H(x)=3x. The given input is 280 because 280 properties were sold last year. Substituting gives H(280)=3(280)=840. That means 840 property sales are expected this year. The answer choice must show the correct input of 280 and the correct output of 840. The other options either reverse the values or use an incorrect output. Therefore, the correct answer is C.
NEW QUESTION # 45
Based on collected data, the number of registered voters in a district can be modeled using the function f(x)=1,300× # 0.92 #
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