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: 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 Describe the patterns shown by the erosion data measurements shown for each of the beaches in the table. Between which years will the beaches have approximately the same width? Assuming these rates remain constant, what can you do to get a better approximation of when the two beaches will have the same width?

1. Western erodes 2 ft/yr; Dunes builds up at 5 ft/yr

2. Sometime in 2006

3. Solve simultaneous equations

Step-by-step explanation:

1. Erosion patterns

(a) Western Beach

In 15 yr, Western Beach erodes from 100 ft to 70 ft.

The rate of erosion is 30 ft/15 yr = 2 ft/yr.

(b) Dunes Beach

In 15 yr, Dunes Beach builds up from 20 ft to 95 ft.

The rate of buildup is 75 ft/15 yr = 5 ft/yr.

2. Beaches with equal width

From the table, it appears that the beaches will have the same width sometime in year 11 (2006).

3. Best approximation

The graph below also shows that it happens part way through year 11 (2006).

We could get an even better solution by calculating the equations of the two lines and solving the simultaneous equations.

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