Answer:
A) ![V(t) = 137750-5500t](https://tex.z-dn.net/?f=V%28t%29%20%3D%20137750-5500t)
B) The value of bulldozer after 3 years is $121250
Step-by-step explanation:
We are given the following in the question:
Cost of bulldozer = $137750
The value of bulldozer depreciates linearly.
A) Let V(t) be the linear function that gives the depreciated value of bulldozer after t years. Then, we can write:
![V(t) = a +bt](https://tex.z-dn.net/?f=V%28t%29%20%3D%20a%20%2Bbt)
Cost of new bulldozer = $137750
![V(0) =137750\\a + b(0) = 137750\\\Rightarrow a = 137750](https://tex.z-dn.net/?f=V%280%29%20%3D137750%5C%5Ca%20%2B%20b%280%29%20%3D%20137750%5C%5C%5CRightarrow%20a%20%3D%20137750)
Value of bulldozer at the end of 22 years = $16750
![V(22) =16750\\a + b(22) = 16750\\\Rightarrow 137750 + 22b = 16750\\\\\Rightarrow b = \dfrac{16750-137750}{22} =-5500](https://tex.z-dn.net/?f=V%2822%29%20%3D16750%5C%5Ca%20%2B%20b%2822%29%20%3D%2016750%5C%5C%5CRightarrow%20137750%20%2B%2022b%20%3D%2016750%5C%5C%5C%5C%5CRightarrow%20b%20%3D%20%5Cdfrac%7B16750-137750%7D%7B22%7D%20%20%3D-5500)
Thus, the value of bulldozer is given by the function V(t)
![V(t) = 137750-5500t](https://tex.z-dn.net/?f=V%28t%29%20%3D%20137750-5500t)
where t is time in years.
B) Value of bulldozer after 3 years
We put t = 3 in the equation.
![V(3) = 137750-5500(3)=121250](https://tex.z-dn.net/?f=V%283%29%20%3D%20137750-5500%283%29%3D121250)
Thus, the value of bulldozer after 3 years is $121250