A bulldozer costs $120,000 and each year it depreciates 8% of its original value. Find a formula(equation) for the value V of the bulldozer after t years.
how about
v = 120000 * 0.92^t
??
To find the formula for the value V of the bulldozer after t years, we need to consider that each year the bulldozer depreciates 8% of its original value.
Let's break down the problem step by step:
1. Start with the original value of the bulldozer, which is $120,000.
2. In the first year, the bulldozer will lose 8% of its original value. We can calculate the depreciation as follows: 8% of $120,000 = $9,600.
3. After one year of depreciation, the value of the bulldozer will be $120,000 - $9,600 = $110,400.
4. In the second year, the bulldozer will lose 8% of this new value. Again, we can calculate the depreciation: 8% of $110,400 = $8,832.
5. After the second year of depreciation, the value of the bulldozer will be $110,400 - $8,832 = $101,568.
We can see that the value of the bulldozer after each year follows a pattern. It decreases by 8% each year, meaning it is multiplied by a factor of 0.92 (100% - 8% = 92%).
Now, to find the formula for the value V of the bulldozer after t years, we can use basic exponential decay formula:
V = original value × (depreciation factor)^t
In this case, the original value is $120,000, and the depreciation factor is 0.92 (92% expressed as a decimal):
V = $120,000 × 0.92^t
This gives us the formula for the value V of the bulldozer after t years as V = $120,000 × 0.92^t.