1. Find the formula for the linear depreciation of the value of an automobile from $25,000 to $20,450 in 7 years.
Answer: V(t) = 25,000 - 650 (t), t = years and V in $
2. A farm equipment depreciates according to a linear
model.
If after the 2nd year the value is $25,000 and
after the 7th year its value is $12,500,
what is the best formula that describes this depreciation?
Answer: V(t) = 30,000 - 2500 (t), t = years and V in $
3. An office machine decreases in value from $25,000
to $16,211.94 over a 7 year period.
If the decrease is exponential, write a formula
for the value of the machine over time.
Answer: V(t) = 25,000 (0.94)t
, rate r is 6 % per year for t years, V in $
k = ln (0.94) = -0.0619..
or V(t) = 25,000 e-0.0619 t , where k is the continuous rate at -6.19 %
Remember negative values of k means the function is decreasing
4. The cost of an item decreases over time exponentially.
If its cost was observed to be $8,500 at year 1
and $3205.77 at year 7, what is the formula that
best describe this depreciation?
Answer: C(t) = 10,000 (0.85)t , rate r is 15 % per year for t years, C is cost in $
or C(t) = 10,000 e-0.1625 t , where k is the continuous rate at -16.25 %
5. If an experimental solar equipment depreciates
for tax purposes at a rate of 10% every 10 years,
What is its depreciated value at the end of 20
years?
Answer: V(t) = 100,000 (0.90)2 = $81,000 , rate, r is 10 % per year for t =10 year periods
An equivalent solution leading to same results V(t)*
= 100,000 e-0.105360515 x 2 = $81,000 ,where
k = -0.1054 at -10.54 %
* note that the wording of problem 5 precludes this approach since it specifically
states that the increase is periodic