Question

A restaurant purchases a pizza oven for $6400. After 1 year, its depreciated value is $5810. The depreciation is linear.

(a)
Write a linear model that relates the value V of the oven to the time t in years.

Answer 1

The linear model that relates the value V of the oven to the time t in years is V = -590t + 6400, where V is the value of the oven and t is the time in years. The slope of the model is -590, indicating a decrease in value over time. The y-intercept of the model is 6400, representing the initial cost of the oven.

Step-by-step explanation:

To write a linear model that relates the value V of the oven to the time t in years, we can use the slope-intercept form of a linear equation: V = mt + b.

In this case, the initial value is $6400 (the cost of the oven) and the depreciated value after 1 year is $5810.

So, we have the points (1, 5810) and (0, 6400).

To find the slope m, we can use the formula: m = (y2 - y1) / (x2 - x1).

Plugging in the values, we get: m = (5810 - 6400) / (1 - 0) = -590.

Now, we can substitute the slope m and one of the points into the equation to find the y-intercept b.

Using the point (1, 5810): 5810 = -590 * 1 + b.

Solving for b, we get: b = 6400.

Therefore, the linear model that relates the value V of the oven to the time t in years is: V = -590t + 6400.