car: use the graph and table to answer the questions. which vehicle loses the most value each year? which…

Explanation:

Step1: Calculate car's annual - depreciation

The car has an initial value of $y_1 = 20000$ at $x_1 = 0$ and a value of $y_2=10900$ at $x_2 = 6$. The annual - depreciation $d_{car}$ is calculated using the formula $d=\frac{y_1 - y_2}{x_2 - x_1}$. So, $d_{car}=\frac{20000 - 10900}{6}=\frac{9100}{6}\approx1516.67$.

Step2: Calculate truck's annual - depreciation

The truck has an initial value of $y_1 = 21000$ at $x_1 = 0$ and a value of $y_2 = 14400$ at $x_2 = 6$. The annual - depreciation $d_{truck}$ is calculated using the formula $d=\frac{y_1 - y_2}{x_2 - x_1}$. So, $d_{truck}=\frac{21000 - 14400}{6}=\frac{6600}{6}=1100$. Since $1516.67>1100$, the car loses the most value each year.

Step3: Calculate time for car to lose all value

Let the initial value of the car $V_{0 - car}=20000$ and the annual - depreciation $d_{car}\approx1516.67$. The time $t_{car}$ to lose all value is $t_{car}=\frac{20000}{1516.67}\approx13.2$.

Step4: Calculate time for truck to lose all value

Let the initial value of the truck $V_{0 - truck}=21000$ and the annual - depreciation $d_{truck}=1100$. The time $t_{truck}$ to lose all value is $t_{truck}=\frac{21000}{1100}\approx19.09$. So the car will lose all of its value first.

Step5: Calculate new time for truck to lose all value

If the truck's rate of depreciation changes to $d_{new - truck}=1650$, and the initial value $V_{0 - truck}=21000$. The time $t_{new - truck}$ to lose all value is $t_{new - truck}=\frac{21000}{1650}\approx12.73$. Since $12.73<13.2$, the truck will lose all of its value first.

Answer:

Which vehicle loses the most value each year? Car Which vehicle will lose all of its value first? Car If the truck’s rate of depreciation changes to a decrease of $1,650$ each year, which vehicle will lose all of its value first? Truck