Final answer:
The value of the equipment after t years can be represented by the linear equation V = -2,500t + 27,000. This equation takes into account the initial purchase price of $27,000, the final value of $2,000, and a straight-line depreciation rate of $2,500 per year over 10 years.
Step-by-step explanation:
To write a linear equation giving the value V of the equipment during the 10 years it will be in use, we need to understand the initial value, final value, and the rate of depreciation over time. The initial value of the equipment is $27,000, and after 10 years, its value is expected to be $2,000. This means the equipment loses value at a constant rate each year, which is the characteristic of linear depreciation.
Let t be the number of years after purchase, and V be the value of the equipment at time t. The rate of depreciation per year is calculated as the change in value divided by the number of years, so:
Depreciation rate = (Initial value - Final value) / Number of years
Depreciation rate = ($27,000 - $2,000) / 10 = $25,000 / 10 = $2,500 per year.
The linear depreciation model can be expressed in the form of the equation V = mt + b, where m is the slope (rate of depreciation) and b is the y-intercept (initial value). In this case, m is negative because the value is decreasing over time.
The equation representing the value of the equipment V after t years is:
V = -2,500t + 27,000
Here, -2,500 represents the depreciation rate, and 27,000 is the initial value of the equipment.