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. Western beach width Dunes beach
Year number (in feet) width (in feet)
0 100 20
5 90 45
10 80 70
11 78 75
12 76 80
15 70 95
Assuming these rates remain constant, what can you do to get a better approximation of when the two beaches will have the same width?
To get a better approximation of when the two beaches will have the same width, you can calculate the rate of erosion for each beach and use that information to estimate when their widths will be equal.
To calculate the rate of erosion for each beach, you need to determine the change in width divided by the change in years.
For the Western beach:
Rate of erosion = (Initial width - Final width) / (Final year - Initial year)
Using the provided data:
Initial width = 100 feet
Final width = 70 feet
Initial year = 0
Final year = 15
Rate of erosion for the Western beach = (100 - 70) / (15 - 0) = 30 / 15 = 2 feet per year
For the Dunes beach:
Rate of erosion = (Initial width - Final width) / (Final year - Initial year)
Using the provided data:
Initial width = 20 feet
Final width = 95 feet
Initial year = 0
Final year = 15
Rate of erosion for the Dunes beach = (20 - 95) / (15 - 0) = -75 / 15 = -5 feet per year
Now that you have the erosion rates for both beaches, you can estimate when their widths will be equal by using the equation:
Width of Western beach = Width of Dunes beach
Let's solve for time (years) when the widths will be equal, assuming the rates of erosion remain constant:
Initial width of Western beach + (Rate of erosion for Western beach * time) = Initial width of Dunes beach + (Rate of erosion for Dunes beach * time)
100 + (2 * time) = 20 + (-5 * time)
Solving this equation will give you the estimated time when the two beaches will have the same width.
To get a better approximation of when the two beaches will have the same width, you can calculate the rate of change for each beach and then use that information to make projections.
1. First, calculate the rate of change for each beach by determining how much the width of the beach changes over a specific period (e.g., every year). This can be done by subtracting the initial width from the final width and dividing it by the number of years.
For the Western beach:
- Rate of change = (Final Width - Initial Width) / Number of Years
For example, for the Western beach between year 0 and year 15:
- Rate of change = (70 - 100) / 15 = -2 ft/year
Similarly, calculate the rate of change for the Dunes beach using the same formula.
2. Once you have the rates of change for each beach, you can assume that these rates will remain constant in the future. This assumption allows us to make projections about when the two beaches will have the same width.
3. For each beach, calculate the number of years it will take for the width to reach the same value as the other beach. This can be done by dividing the difference in current widths by the rate of change for that beach.
For example, if the current width of the Western beach is 70 feet and the rate of change is -2 ft/year, and the current width of the Dunes beach is 95 feet with a rate of change of -5 ft/year:
- Time for Western beach to match Dunes beach width = (95 - 70) / (-2) = 12.5 years
- Time for Dunes beach to match Western beach width = (70 - 95) / (-5) = 5 years
These calculations provide an approximation of when the two beaches will have the same width based on the assumption of constant rates of change. Keep in mind that actual erosion rates may not remain constant, so this is only an estimate. Regular monitoring and updating of data will provide more accurate information about changes in beach widths.
graph them and see where the curves intersect
Hi Hannah,
Since this question is part of a graded assignment, you should not be asking for help online.