Question

A restaurant purchased a pizza oven for $6500. After 1 year, its depreciated value is $5850. The depreciation is linear

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

Use the model to estimate the value of the oven after 3 years

Answer 1

To write a linear model for the depreciation of the pizza oven, we can use the formula for a line, which is y = mx + b. In this formula, y represents the value of the oven, x represents the time in years, m is the slope of the line (representing the rate of depreciation per year), and b is the y-intercept (representing the initial value of the oven).

Given that the oven's initial value is $6500 and its value after 1 year is $5850, we can find the slope (m) of the line using the formula:

m = (change in value) / (change in time) = (5850 - 6500) / (1 - 0) = -650 / 1 = -650.

Therefore, the linear model for the depreciation of the oven is V(t) = -650t + 6500, where V(t) represents the value of the oven after t years.

To estimate the value of the oven after 3 years (t = 3), substitute t = 3 into the equation:

V(3) = -650(3) + 6500 = -1950 + 6500 = 4550.

Therefore, the estimated value of the oven after 3 years is $4550.

Answer 2

V = 6500 - 650t

Value after 3 years = $4550

Explanation:

Calculate the decrease in price by subtracting the present cost from the cost of the oven at the time of purchase.

Decreased amount = 6500 - 5850

= $650

$650 is the amount of depreciation every year. so, for 't' years it will be 650*t = 650t

To calculate the value of the oven after 't' years, subtract 650t from 6500.

Cost of the oven after 't' years = cost at the time of purchase - the amount of depreciation in 't' years.

`\sf \boxed{\bf V = 6500 - 650t}`

Now, t = 3

V = 6500 - 650*3

= 6500 - 1950

= $ 4550

Answer:

Value of oven after 3 years = $ 4550