You have just won the lottery (or perhaps were chosen in the 1^st round of the N

Question

You have just won the lottery (or perhaps were chosen in the 1^st round of the NBA draft), and are going to use some of your windfall to build yourself a dream house on the Oregon Coast. The property you have chosen sits on top of a cliff with a spectacular view of the ocean. You would like to build your mansion as close to the cliff edge as possible, but erosion of the sea cliff is such that the cliff edge is retreating front the sea at an average rate of 30 cm/yr. In accordance with your building permit, the outermost wall of your house must be at least 20 feet (6.1 m) from the cliff edge, and since you want the best possible view, you build it exactly at live 20-feet mark. What is the average retreat rate of the cliff in inches year At the average retreat rate, how long until the cliff lace retreats to the wall of your house (at which time you will probably want to move out)? Assume that you can find special "erosion insurance" that costs $3000 yr for a house within 8 m of a sea cliff, but costs $4000 yr for a house within 2 m of a sea cliff. How long until erosion reduces your original 6.1 m setback to only 2 m and your insurance rate goes up?

Explanation / Answer

1) 12 inches/year

2) distance between cliff edge and wall= 20feet= 6.1m= 610cm.

Rate of cliff edge retreat= 30cm/yr.

Time taken for cliff edge to retreat to the wall= 610/30= 20.34years

3) time taken for cliff edge to retreat by 4.1m(6.1-2)= 410/30= 13.67years.

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