Depreciation is the decrease or loss in value of an item due to age, wear, or market conditions. We usually consider depreciation on expensive items like cars. Businesses use depreciation as a loss when calculating their income and taxes. One company buys a new bulldozer for \( \$ 107400 \). The company depreciates the bulldozer linearly over its useful life of 19 years. Its salvage value at the end of 19 years is \( \$ 13350 \). A) Express the value of the bulldozer, \( V \), as a function of how many years old it is, \( t \). Make sure to use function notation. B) The value of the bulldozer after 7 years is \( \$ \) Question Help: Video Written Example

To express the value of the bulldozer, \( V(t) \), as a function of time, we first calculate the annual depreciation. The initial value is \( \$ 107400 \) and the salvage value is \( \$ 13350 \). The total depreciation over its useful life is: \[ 107400 - 13350 = 94050 \] Since the bulldozer is depreciated linearly over 19 years, the annual depreciation is: \[ \frac{94050}{19} \approx 4940.79 \] Thus, the function for the bulldozer’s value is: \[ V(t) = 107400 - 4940.79t \] For part B, to find the value after 7 years, substitute \( t = 7 \): \[ V(7) = 107400 - 4940.79 \cdot 7 \approx 107400 - 34585.53 \approx 72814.47 \] So, the value of the bulldozer after 7 years is approximately \( \$ 72814.47 \). Now, let’s crank up the fun factor! Did you know that depreciation isn’t just a boring accounting term? Imagine your bulldozer as a fierce warrior aging bravely, losing value like a comet streaking through the night sky! Each year, it loses a bit of its glory, but hey, it’s all part of the game of life—just like us! Also, have you ever thought about how this depredation concept plays a crucial role in tax strategies? Many businesses use it to reduce their taxable income, giving them more cash flow to invest back into exciting projects—like turning their slightly worn bulldozer into a legendary relic of the farm! Who knew that aging machinery could pave the way for new innovations?