Answer:
<h2>The time needed is 10 months.</h2>
Step-by-step explanation:
The given points are (0, 3500) and (5, 1750).
First, we use the formula below to find the slope of the line
![m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }=\frac{1750-3500}{5-0}=\frac{-1750}{5}=-350](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%20%20%7D%7Bx_%7B2%7D%20-x_%7B1%7D%20%7D%3D%5Cfrac%7B1750-3500%7D%7B5-0%7D%3D%5Cfrac%7B-1750%7D%7B5%7D%3D-350)
Which means the function is deacrasing with a ratio of 350 feet per month.
Now, we use the slope and one point to find the equation
![y-y_{1} =m(x-x_{1} )\\y-1750=-350(x-5)\\y=-350x+1750+1750\\y=-350x+3500](https://tex.z-dn.net/?f=y-y_%7B1%7D%20%3Dm%28x-x_%7B1%7D%20%29%5C%5Cy-1750%3D-350%28x-5%29%5C%5Cy%3D-350x%2B1750%2B1750%5C%5Cy%3D-350x%2B3500)
This linear function shows that the situation started at the y-intecept (0, 3500), which means the month 0 had already 3500 feet. In other words, the total distance is 3500 feet. Now, the x-intercept will tell us the time needed to travel that distance.
![0=-350x+3500\\-3500=-350x\\x=\frac{-3500}{-350}\\ x=10](https://tex.z-dn.net/?f=0%3D-350x%2B3500%5C%5C-3500%3D-350x%5C%5Cx%3D%5Cfrac%7B-3500%7D%7B-350%7D%5C%5C%20x%3D10)
Therefore, the time needed is 10 months.