Solving systems of equations aooriximately

  1. Complete the table below to solve the equation 2.5x – 10.5 = 64(0.5x).
    x f(x) = 2.5x – 10.5 g(x) = 64(0.5x)
  2. 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.

    Graph with x axis labeled years. Y axis labeled revenue in dollars. The line for printed ad revenue starts at 0, 3 and goes through the10, 2. The line for online ad revenue starts at 0, 0 zero and goes through the 10, 3.

  3. 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. 
    Year number Western Beach width (in feet) Dunes Beach width (in feet)
    0 100 20
    5 90 45
    10 80 70
    11 78 75
    12 76 80
    15 70 95

    1. Describe the patterns shown by the erosion data measurements shown for each of the beaches in the table.
    2. Between which years will the beaches have approximately the same width?
    3. Assuming these rates remain constant, what can you do to get a better approximation of when the two beaches will have the same width?
  4. 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:
    1. Write two functions to model this situation, and graph those two functions on the same coordinate grid.
    2. During what year in the future will the park have approximately the same number of pine and oak trees?
    3. How many of each type of tree will there be at that time?