Question

Two ocean beaches are being affected by erosion. The table shows the width, in feet, of each beach measured at high tide where 1995 is represented by year 0
A: Describe the patterns shown by the erosion data measurements shown for each of the beaches in the table.


B: Between which years will the beaches have approximately the same width?


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

Answer 1

Answer:

A: Linear

B: 11 and 12

C: Finding the common point to the derived equations of the erosion effect on the width of the beaches

Step-by-step explanation:

A: The pattern shows a linear pattern relationship between the widening of the beach due to erosion effect and the number of years with an increasing  widening with time for Dunes beach while Western beach increasingly narrows with time

B: From the data, and from plotting the graph of the data, the beaches will have approximately the same width between 11 and 12 years

C: A better approximation can be obtained by deriving an equation for the relationship between the widening of the beaches with time and finding the common solution to the equations as follows;

From Excel

Dunes beach equation

y = 5·x + 20

Western beach equation

y = -2·x + 100

The point of intersection is found from equating both y-values equations as follows;

5·x + 20 = -2·x + 100

5·x +2·x=   100- 20

7·x  = 80

x = 80/7 = 11.42 years