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| Section | Objectives |
|---|---|
| Topic 1: Graphical Depictions | - Interpret maximum and minimum for situations - Interpret concavity for situations - Interpret rates of change for situations - Interpret inputs and outputs for situations - Interpret asymptotes for situations |
| Topic 2: Validity of Models | - Examine utility - Determine fit - Determine validity |
| Topic 3: Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
| Topic 4: Exponential Functions | - Interpret inputs and outputs for exponential functions - Interpret rates of change for exponential functions - Interpret concavity for exponential functions |
| Topic 5: Functions and Algebra of Functions | - Derive conclusions based on notation - Derive conclusions based on graphs - Derive conclusions based on data |
| Topic 6: Polynomial Functions | - Interpret inputs and outputs for polynomial functions - Interpret rates of change for polynomial functions - Interpret concavity for polynomial functions |
| Topic 7: Logistic Functions | - Interpret asymptotes for logistic functions - Interpret inputs and outputs for logistic functions - Interpret rates of change for logistic functions |
The function P(t) represents the yearly profit, in millions of dollars, for a clothing store since opening. The graph of P(t) is shown.
How should the maximum value be interpreted?
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The function N(t)models the number of subscribers to a virtual newsletter over time. The graph of N(t)is shown. The horizontal axis represents the number of years since the newsletter started, and the vertical axis represents the number of subscribers, in thousands.
How is the number of subscribers changing over time based on the graph?
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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)?
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The graphed function n(t)represents the number of animals, n, at a feeding station thours after 5:00 a.m. The plotted points Aand Bhave coordinates (1#10.6)and (8#6.59).
Which statement gives the correct interpretation of the average rate of change of the number of animals over the interval from point Ato point B?
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The exponential function
f(t)=2900(1.13)
t
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How many bacteria are in the population when t=18?
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