Question

A restaurant purchases a pizza oven for $6500. after 1 year, its depreciated value is $5860. the depreciation is linear. write a linear model that relates the value v of the oven to the time t in years.

Answer 1

The linear model for the depreciating value of the oven based on linear depreciation is v = -640t + 6500, where t is time in years.

Step-by-step explanation:

To write a linear model that relates the value v of the oven to the time t in years, let's start with the information provided. The initial value of the pizza oven is $6500 and after 1 year, the value is $5860. We'll use the standard form of a linear equation, which is v = mt + b, where m is the slope and b is the y-intercept.

First, we calculate the annual depreciation by subtracting the value after 1 year from the initial value:
$6500 - $5860 = $640. Next, we determine the slope (m) which represents the rate of depreciation per year. Since the oven loses $640 in value over the span of one year, the slope is -640. The y-intercept (b) is the initial value of the oven, which is $6500.

Therefore, the linear model for the depreciating value of the oven is v = -640t + 6500.