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?
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 =
where (x1,y1) = (0,600)
and where (x2,y2) = (1,545)
m =
m =
m = -55
Point-slope formula:
y - y1 = m(x - x1)
where (x1,y1) = (0,600) and m = -55
y - 600 = -55(x - 0)
y - 600 = -55x
y = -55x + 600
What is the bicycle’s value after 3.5 years?
Plug in 3.5 years for x, solve for y dollars:
y = -55(3.5) + 600
y = $407.50
How long before the bicycle is worth zero?
Plug in 0 dollars for y, solve for x years.
0 = -55x + 600
55x = 600
x = 600/55 = years.
Edwin