The graphs show the percentage of high school seniors who...

The graphs show the percentage of high school seniors who had ever used alcohol or marijuana. (GRAPH CANT COPY) The data for the graphs at the bottom of the previous page can be described by the following mathematical models: (GRAPH CANT COPY) a. Use the appropriate line graph to estimate the percentage of seniors who used alcohol in 2014 . b. Use the appropriate formula to determine the percentage of seniors who used alcohol in 2014 . How does this compare with your estimate in part (a)? c. Use the appropriate line graph to estimate the percentage of seniors who used marijuana in 2014 . d. Use the appropriate formula to determine the percentage of seniors who used marijuana in 2014 . How does this compare with your estimate in part (c)? e. For the period from 1990 through 2014 , in which year was alcohol use by seniors at a maximum? What percentage of seniors used alcohol in that year?

The graphs show the percentage of high school seniors who had ever used alcohol or marijuana.
(GRAPH CANT COPY)
The data for the graphs at the bottom of the previous page can be described by the following mathematical models:
(GRAPH CANT COPY)
a. Use the appropriate line graph to estimate the percentage of seniors who used alcohol in 2014 .
b. Use the appropriate formula to determine the percentage of seniors who used alcohol in 2014 . How does this compare with your estimate in part (a)?
c. Use the appropriate line graph to estimate the percentage of seniors who used marijuana in 2014 .
d. Use the appropriate formula to determine the percentage of seniors who used marijuana in 2014 . How does this compare with your estimate in part (c)?
e. For the period from 1990 through 2014 , in which year was alcohol use by seniors at a maximum? What percentage of seniors used alcohol in that year?

Key Concepts

Data Interpretation from Graphs

This concept involves analyzing visual representations of data, such as line graphs, to extract meaningful information. It requires understanding scales, trends, and relationships depicted in a graph. In the context of the problem, it means using a line graph to estimate the percentage values at specific years, which is a key skill in understanding and communicating data visually.

Mathematical Modeling

Mathematical modeling involves creating and using algebraic expressions or functions to represent real-world phenomena. In this problem, given algebraic formulas are used to calculate the percentages of seniors using substances over time. This concept bridges concrete data representations, like graphs, with abstract mathematical functions that can predict or model trends accurately.

Graphical Estimation Techniques

Graphical estimation is the technique of approximating the value of a function at a specific point by analyzing its graphical representation. By visually inspecting a graph, one can make educated guesses about the numerical outcomes without performing precise calculations, which is useful for quick assessments or when precise data points are not provided.

Algebraic Evaluation of Functions

This concept focuses on computing specific values using given mathematical formulas. By substituting particular inputs (such as a specific year) into the algebraic model, one can precisely determine the corresponding output, such as the percentage of seniors using a substance. This method provides a numerical check against estimated values obtained from graphs.

Comparative Analysis of Methods

Comparing results obtained from different methods, such as graphical estimation and algebraic calculation, is important to verify accuracy and consistency. In the problem, this involves assessing how closely the estimated percentages from the graph align with the calculated percentages from the mathematical model, representing a critical evaluation of different data analysis approaches.

Determining Maximum Values

Identifying the maximum or peak value in a dataset requires analyzing either the graph or the function's behavior over a given interval. This concept includes understanding the idea of optimization, where one finds the year where a certain behavior (like substance use) is at its highest, based on either the visual graph or the computed values from the algebraic model.

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