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 = 80,000 - 6000t. t years.
To find the value of the bus as a function of time, we need to determine the worth of the bus at different points in time, considering the given depreciation rate. In this case, the bus depreciates at a rate of $6,000 per year.
Let's start with the initial value of the bus, which is $80,000. After each year, the value of the bus decreases by $6,000. So, after the first year, the value of the bus will be $80,000 - $6,000 = $74,000.
Using this pattern, we can determine the value of the bus at different points in time. Let's create a function v(t) to represent the value of the bus as a function of time (t), where 0 ≤ t ≤ 10.
When t = 0, the value of the bus is $80,000.
When t = 1, the value of the bus is $74,000.
When t = 2, the value of the bus is $68,000.
When t = 3, the value of the bus is $62,000.
And so on...
We can see that the value of the bus decreases by $6,000 each year. Therefore, we can write the function v(t) as:
v(t) = $80,000 - $6,000t
This function represents the value of the bus as a function of time for 0 ≤ t ≤ 10, assuming straight-line depreciation at a rate of $6,000 per year.