A truck costs $60,000. It depreciates in value $6,000 per year. Write a linear model in the form v(t)=mt+b, where v(t) represents the current value of the truck after t years of ownership
what is v when t=0? That is b.
m is the slope, or how much it changes each year
To write a linear model for the depreciation of the truck, we need to determine the slope (m) and the y-intercept (b) based on the given information.
The truck depreciates $6,000 per year, which means that after t years, the truck's value decreases by 6000t dollars. However, we need to find the current value after t years, so we subtract this depreciation from the initial value of $60,000.
Therefore, the linear model representing the current value (v(t)) of the truck after t years of ownership is:
v(t) = -6000t + 60000
Here, the slope (m) is -6000 and the y-intercept (b) is 60000.
To write a linear model for the given scenario, we need to consider the initial value of the truck and the rate at which it depreciates.
Given:
Initial value (b) = $60,000
Depreciation per year (m) = -$6,000 (since it depreciates, the amount is negative)
The linear model is represented as:
v(t) = mt + b
Substituting the given values, we have:
v(t) = -6000t + 60000
This equation represents the current value of the truck (v) after t years of ownership.