Step-by-step explanation:
Given the equation, V = -1800t + 20,000, where:
V = the value of a car in dollars
t = the number of years after the car's purchase
The y-intercept in the given equation is 20,000, which represents the initial value of the car. It is at this point where t = 0, representing the same time as the car was purchased.
The slope is -1800, which represents the amount for which the car depreciates in value.
In order to determine the time, t, will be worth $11,000, we must substitute its value into the variable, V.
V = -1800t + 20,000
$11,000 = -1800t + 20,000
Subtract 20,000 from both sides:
$11,000 - 20,000 = -1800t + 20,000 - 20,000
- $9,000 = -1,800t
Divide both sides by -1,800 to solve for t:
[tex]\frac{-9,000}{-1800} = \frac{-1800t}{-1800}[/tex]
t = 5
Therefore, the car will be worth $11,000 in 5 years. Understanding these types of information allows us to evaluate our finances and make informed purchase decisions. Certain types of assets such as cars and equipment tend to depreciate (or decrease) in value over time, while investing in a Certificate of Deposits (CDs) tends to appreciate (or increase) in value over time.
