A bus was purchased for $80,000. Assuming the bus depreciates at a rate of $6,000 per year (straight-line depreciation) for the first 10 years, write the value v of the bus as a function of the time t (measured in years) for 0 ¡Ü t ¡Ü 10.
See previous post.
To find the value v of the bus as a function of time t, we can use straight-line depreciation. Straight-line depreciation means that the value of the bus decreases by the same amount each year.
In this case, the bus was purchased for $80,000, and it depreciates at a rate of $6,000 per year for the first 10 years. Since the bus depreciates by $6,000 per year, we can subtract $6,000 from the initial value of $80,000 for each year.
So, for the first year, the value v of the bus is:
v(1) = 80,000 - 6,000
For the second year, the value v of the bus is:
v(2) = v(1) - 6,000 = (80,000 - 6,000) - 6,000
Following this pattern, we can continue calculating the value v of the bus for each year until t = 10.
v(t) = v(t-1) - 6,000
Using this recursive formula, we can calculate the value of the bus for each year from 0 to 10.
v(0) = 80,000
v(1) = v(0) - 6,000
v(2) = v(1) - 6,000
...
v(10) = v(9) - 6,000
So, the value v of the bus as a function of time t for 0 ≤ t ≤ 10 is:
v(t) = 80,000 - 6,000t