Answer:
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
[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }=\frac{1750-3500}{5-0}=\frac{-1750}{5}=-350[/tex]
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
[tex]y-y_{1} =m(x-x_{1} )\\y-1750=-350(x-5)\\y=-350x+1750+1750\\y=-350x+3500[/tex]
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.
[tex]0=-350x+3500\\-3500=-350x\\x=\frac{-3500}{-350}\\ x=10[/tex]
Therefore, the time needed is 10 months.
