Review the grading rubric and use the following information to complete your assignment.

  1. Complete the table below to solve the equation 2.5x – 10.5 = 64(0.5x).

X / F(x) = 2.5x – 10 / G(x) = 64(0.5x)
2 / -5 / 16
3 / -2.5 / 8
4 / 0 / 4
5 / 2.5 / 2
6 / 5 / 1

2.5x – 10.5 = 64(0.5x).

The best approximation for x would be a number between 4 and 5.

  1. A newspaper started an online version of its paper 14 years ago. In a recent presentation to stockholders, the lead marketing executive states that the revenues for online ads have more than doubled that of the revenues for printed ads since starting the online version of the paper. Use the graph below to justify the lead executive’s statement and to determine the approximate year that the two ad revenues were equal.
    They had the same revenue at approximately 7.5 years. The lead executive’s statement would be correct because the graph shows that the printed ads went down to approximately 1.5, and the website ads went up to approximately 4.5, which is more than double the printed ads decrease.
  2. Two ocean beaches are being affected by erosion. The table shows the width, in feet, of each beach at high tide measured where 1995 is represented by year 0.
  3. Describe the patterns shown by the erosion data measurements shown for each of the beaches in the table. The Western Beach decreases its width at 2 feet per year, while the dunes beach increases at 5 feet per year.
  4. Between which years will the beaches have approximately the same width?

Between the years 11 and 12.

  1. Assuming these rates remain constant, what can you do to get a better approximation of when the two beaches will have the same width?

Write a function for each

F(x) would be for Western F(x) = -2x + 100

G(x) would be for Dunes G(x) = 5x + 100

You then have to make the equations equal to each other: -2x + 100 = 5x + 20, and solve for x.

The answer is approximately 11.43 Years

  1. A wooded area in a state park has a mixture of different types of trees. There are 800 pine trees and 50 oak trees. The number of pine trees is decreasing at a rate of 5% per year. The number of oak trees is increasing at a rate of 15% per year. If these trends continue:
  2. Write two functions to model this situation and graph those two functions on the same coordinate grid.

Pine: F(x) = 800(0.95)x Oak: G(x) = 50(1.15)x

  1. During what year in the future will the park have approximately the same number of pine and oak trees?

Approximately at 14.5 years

  1. How many of each type of tree will there be at that time?

There will approximately be 380 trees of each type