Answer:
Part A) ![V(t)=-5,750t+101,250](https://tex.z-dn.net/?f=V%28t%29%3D-5%2C750t%2B101%2C250)
Part B) ![\$55,250](https://tex.z-dn.net/?f=%5C%2455%2C250)
Step-by-step explanation:
Part A) Express the value of the bulldozer, V, as a function of how many years old it is, t.
Let
V ----> the value of the bulldozer (dependent variable or output value)
t ----> the number of years (independent variable or input value)
we know that
The linear function in slope intercept form is equal to
![V(t)=mt+b](https://tex.z-dn.net/?f=V%28t%29%3Dmt%2Bb)
we have the ordered pairs
(0,101,250) and (15,15,000)
Find the slope
The formula to calculate the slope between two points is equal to
![m=\frac{y2-y1}{x2-x1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By2-y1%7D%7Bx2-x1%7D)
substitute
![m=\frac{15,000-101,250}{15-0}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B15%2C000-101%2C250%7D%7B15-0%7D)
----> is negative because is a decreasing function
The value of b is the initial value
so
![b=\$101,250](https://tex.z-dn.net/?f=b%3D%5C%24101%2C250)
substitute
![V(t)=-5,750t+101,250](https://tex.z-dn.net/?f=V%28t%29%3D-5%2C750t%2B101%2C250)
Part B) The value of the bulldozer after 8 years is
For t=8 years
substitute the value of t in the linear equation
![V(t)=-5,750(8)+101,250=\$55,250](https://tex.z-dn.net/?f=V%28t%29%3D-5%2C750%288%29%2B101%2C250%3D%5C%2455%2C250)