Question

the 2012 jeep liberty limited sport 2wd has one of the largest depreciation values of any car. suppose a 2012 jeep liberty limited sport 2wd sold for $22,000.00 in 2012 and its value depreciates by $2,300.00 per year. assume the depreciation is linear.
a) let y be the value of the 2012 jeep liberty limited sport 2wd and t be the number of years since 2012. find the equation that represents the price of the car.
b) how much is the car worth in 1 year?
c) how much is the car worth in 2 years?
d) in what year will the value of the car reach $0.00? round up to the nearest whole year.

Explanation:

Step1: Determine the linear - equation form

The general form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. In the context of depreciation, the initial value of the car ($b$) is $22000$ and the rate of depreciation ($m$) is $- 2300$. So the equation is $y=-2300t + 22000$.

Step2: Find the value of the car after 1 year

Substitute $t = 1$ into the equation $y=-2300t + 22000$.
$y=-2300\times1 + 22000=22000 - 2300=19700$.

Step3: Find the value of the car after 2 years

Substitute $t = 2$ into the equation $y=-2300t + 22000$.
$y=-2300\times2+22000=22000 - 4600 = 17400$.

Step4: Find when the car's value is 0

Set $y = 0$ in the equation $y=-2300t + 22000$ and solve for $t$.
$0=-2300t + 22000$.
$2300t=22000$.
$t=\frac{22000}{2300}\approx9.57$. Rounding up, $t = 10$. Since $t$ is the number of years since 2012, the year is $2012 + 10=2022$.

Answer:

a) $y=-2300t + 22000$
b) $19700$
c) $17400$
d) $2022$