Question 280538
to solve your problem, I had to figure out what mill rate means.


Here's a link to a definition.


<a href = "http://en.wikipedia.org/wiki/Property_tax" target = "_blank">http://en.wikipedia.org/wiki/Property_tax</a>


The car is valued at $16,200 3 years after purchase.


The care is valued at $13,800 7 years after purchase.


If we let x = the number of years after purchase, and we let y = the value of the car after x years of purchase, then we have 2 points from which we can draw a straight line and generate an equation for that line.


our points are:


(x1,y1) = (3,16200)
(x2,y2) = 7,13800)


the general form of the slope-intercept form of an equation for a straight line is:


y = mx + b where m is the slope and b is the y-intercept.


First we find the slope:


slope is equal to (y2-y1)/(x2-x1).


This becomes:


m = (13800 - 16200)/(7-3) = -2400 / 4 = -600


The car is depreciating at the rate of $600 per year.


our equation becomes:


y = -600*x + b


Next we need to find the y-intercept.


That's the value of y when x = 0.


To do that, we pick any one of the points on the line.


we could pick (x1,y1) or we can pick (x2,y2).


Either point will yield the same answer for b.


We'll use (x1,y1) = (3,16200)


Our equation of y = -600*x + b becomes 16200 = -600*3 + b which becomes 16200 = -1800 + b.


We add 1800 to both sides of this equation to get:


16200 + 1800 = b which becomes 18000 = b.


Our equation becomes:


y = -600*x + 18000


Now that we have the equation, we can predict the value of the car at the end of 10 years.


We replace x with 10 to get:


y = -600*10 + 18000 which becomes y = -6000 + 18000 which becomes y = 12000.


The car will be worth 12000 at the end of 10 years.


Now we apply the mill rate to that.


A mill rate of 18 means the car will be assessed 18 dollars per thousand dollars of value which would equal a property tax of 18 * 12000 / 1000 = $216 when the car is 10 years old.


A graph of the equation for the value of the car is shown below:


{{{graph(600,600,-5,15,-1000,19000,-600*x+18000,16200,13800,12000)}}}


Horizontal lines have been placed at 16200, 13800, and 12000 to show you that these values occur at 3 years, 7 years, and 10 years respectively.


Just drop a perpendicular line from the intersection of the graph of the equation with these horizontal lines to see that the value of x at those intersections is about where it should be:   3 years for 16200, 7 years for 13800, and 10 years for 12000.