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.
v(t)= _____
To find the value of the bus as a function of time, we need to start with the initial value of the bus and subtract the depreciation for each year.
Given:
Initial value of the bus (t=0): $80,000
Depreciation per year: $6,000
Since the depreciation is a constant rate of $6,000 per year, we can use the formula for straight-line depreciation:
Depreciation per year = (Initial value - Final value) / Number of years
In this case, the initial value is $80,000 and the final value is what we want to find. The number of years is 10.
$6,000 = ($80,000 - Final value) / 10
To find the final value (v), we can rearrange the equation:
$6,000 * 10 = $80,000 - Final value
$60,000 = $80,000 - Final value
Now, let's solve for the final value:
Final value = $80,000 - $60,000
Final value = $20,000
Therefore, the value (v) of the bus as a function of time (t) for 0 ≤ t ≤ 10 is:
v(t) = $80,000 - ($6,000 * t) for 0 ≤ t ≤ 10
So, the final equation is:
v(t) = $80,000 - $6,000t
it drops 6000/year, so you will have -6000t in there somewhere.
v started at 80000
That should do it.