PARCC Math II Unit 2 Lesson 5

Walch Education, 3. 11. 2014

These applets are provided by Walch Education as supplemental material for the [i]CCSS Integrated Pathway: Mathematics II[/i] program. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on our resources.

Obsah

  1. 2.5.1
    1. Example 1
    2. Example 3
  2. 2.5.2
    1. Example 2
    2. Example 3
  3. 2.5.3
    1. Example 2
    2. Example 3

1.

2.5.1

  • 1. Example 1
  • 2. Example 3

1.1.

Example 1

A school tracks the total number of students enrolled each year. The school uses the change in the total number of students to estimate how many students have been enrolled in the school each year since 2000. If [math]t[/math] is the number of years after 2000, the total number of students, [math]f(t)[/math], can be estimated using the function [math]f(t) = 250(0.98)^t[/math]. How is the total number of students changing each year? Is the total number of students growing or decaying?
[list=1][br][*]Identify the yearly rate of change in the function.[br][/*][*]Describe how the rate of change relates to the change of the dependent quantity.[br][/*][*]Determine whether the dependent quantity is growing or decaying.[br][/*][/list][br]This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit [url=http://www.walch.com/]www.walch.com[/url] for more information.
– Walch Education

1.2.

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2.

2.5.2

  • 1. Example 2
  • 2. Example 3

2.1.

Example 2

In the mid-1980s, the U.S. Fish and Wildlife Service began reintroducing gray wolves into regions of the western United States where the wolf population had become endangered. The table that follows shows the approximate number of wolves in a certain region every 2 years since the reintroduction. Two models have been proposed for this data: [math]y = 59x + 10[/math] and [math]y = 16.9(1.22)^x[/math]. Which model best represents the data? Create a residual plot for the model you chose. Use your results to predict the estimated wolf population for this region after another 10 years.

[list=1] [*]Create a scatter plot of the data. [*]Determine which of the two proposed models is appropriate for the data. [*]Create a residual plot for the chosen model. [*]Plot the residuals on a residual plot and determine whether the chosen function is a good model for this situation. [*]Use your results to predict the estimated wolf population in this region after another 10 years. [/list] This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on their resources.
– Walch Education

2.2.

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3.

2.5.3

  • 1. Example 2
  • 2. Example 3

3.1.

Example 2

Three students are shooting wads of paper with a rubber band, aiming for a trash can in the front of the room. The height of each student’s paper wad in feet is given as a function of the time in seconds. Which student’s paper wad flies the highest? • The path of Alejandro’s paper wad is modeled by the equation [math]f(x) = –x^2 + 2x + 7[/math]. • Melissa’s paper wad is estimated to reach the heights shown in the table below. [math]\ \ \ \ \ x \ \ \ 0 \ \ \ 2 \ \ \ 3 \ \ \ 4[/math] [math]\ \ \ \ \ y \ \ \ 3 \ \ \ 6 \ \ \ 7 \ \ \ 6[/math] • After [math]3[/math] seconds, Connor’s paper wad achieves a maximum height of [math]6.5[/math] feet above the floor.

[list=1] [*]Determine if each function represents a quadratic. [*]Verify that the extremum for each function is the maximum value of each function. [*]Determine the vertex of each function. [*]Use the vertices to determine whose paper wad goes the highest. [/list] This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on their resources.
– Walch Education

3.2.

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