A boat was purchased for $45,000. Assuming the boat depreciates at a rate of $4700 per year (straight-line depreciation) for the first 8 years, write the value v of the boat as a function of the time t (measured in years) for 0 ¡Ü t ¡Ü 8.
v(t) = ____, 0 ¡Ü t ¡Ü 8
To find the value of the boat as a function of time, we can use the concept of straight-line depreciation. Straight-line depreciation assumes that the value of the boat decreases by the same amount every year.
In this case, the boat was purchased for $45,000, and it depreciates at a rate of $4,700 per year. We want to find the value of the boat for each year within the range of 0 to 8.
To get the value v(t) of the boat at each time t, we can subtract the amount of depreciation from the initial value.
For the first year (t = 1), the depreciation would be $4,700. So, the value of the boat after 1 year would be:
v(1) = $45,000 - $4,700 = $40,300
For the second year (t = 2), the depreciation would still be $4,700. So, the value of the boat after 2 years would be:
v(2) = $40,300 - $4,700 = $35,600
Similarly, we can calculate the value of the boat for each year up to t = 8.
Using this pattern, we can write the value v of the boat as a function of time t within the range 0 ≤ t ≤ 8:
v(t) = $45,000 - $4,700t, 0 ≤ t ≤ 8