Question 959040
A college professor has purchased a new bicycle for commuting to class.  This 
bicycle had a purchase price of $600 and depreciates at a constant rate of $55 a
year.  What is the bicycle’s value after 3.5 years?  How long before the bicycle
is worth zero?

<pre>
1. When 0 years have passed, the bicycle is worth $600
2. When 1 year has passed, the bicycle is worth $600-$55 = $545

Let x = the number of years that have passed.
Let y = the worth of the bicycle.

Then, the interpretation of the above two sentences are:

1. When x=0, y=600
2. When x=1, y=545

The mathematical interpretation is:

Find the equation of the line that passes through the 
points (0,600) and (1,545)

Slope formula:

m = {{{(y[2]-y[1])/(x[2]-x[1])}}}

where (x<sub>1</sub>,y<sub>1</sub>) = (0,600)
and where (x<sub>2</sub>,y<sub>2</sub>) = (1,545)

m = {{{(545-600)/(1-0)}}}

m = {{{-55/1}}}

m = -55

Point-slope formula:

y - y<sub>1</sub> = m(x - x<sub>1</sub>)

where (x<sub>1</sub>,y<sub>1</sub>) = (0,600) and m = -55

y - 600 = -55(x - 0)

y - 600 = -55x 

y = -55x + 600
</pre>
What is the bicycle’s value after 3.5 years?  
<pre>
Plug in 3.5 years for x, solve for y dollars:

y = -55(3.5) + 600
y = $407.50
</pre>
How long before the bicycle is worth zero? 
<pre>
Plug in 0 dollars for y, solve for x years.

0 = -55x + 600
55x = 600
  x = 600/55 = {{{10&10/11}}} years.

Edwin</pre>