Question

A sand dune stands $5\text{feet}$ above sea level. The hill is eroding at a rate of $1\text{foot}$ per $20\text{years}$. Let $y$ represent the height of the sand dune after $x\text{years}$. Which equation represents the situation?

Answer 1

Linear formation of condition:

It is given that $y$ represent the height of the sand dune after $x\text{years}$ and the hill is eroding at a rate of$1\text{foot}$ per $20\text{years}$.

In a year the hill is eroding $\frac{1}{20}\text{feet}$.

In $x\text{years}$ the hill will erode $\frac{1}{20}\text{feet}$.

It is also given that the total height of sand dune is $5\text{feet}$.

Then after $x\text{years}$ the height will be $y=5-\frac{x}{20}$.

Hence, the equation $y=5-\frac{x}{20}$ represents the situation.