The function that gives the car's value is
![V(t)=5000(1-\frac1{10})^t](/tpl/images/0604/2487/36d8c.png)
where V(t) is in dollar and t is number of years after it sold.
Step-by-step explanation:
Given that,
A car sells for $5000 and losses
of its value each year.
The value of car will loss after 1 year is
![=\$5000 \times \frac1{10}](/tpl/images/0604/2487/4d45c.png)
The price of the car after 1 year is
![=\$(5000-5000\times \frac 1{10})](/tpl/images/0604/2487/83336.png)
![=\$\{5000(1-\frac1{10})\}](/tpl/images/0604/2487/f62c5.png)
![=\$\{5000(1-\frac1{10})^1\}](/tpl/images/0604/2487/5c652.png)
The value car will loss in 2 year is
![=\$\{5000(1-\frac1{10})\times \frac1{10}\}](/tpl/images/0604/2487/d0a43.png)
After 2nd year the car will be
![=\$ \{5000(1-\frac1{10})\}-\{5000(1-\frac1{10})\times \frac1{10}\}](/tpl/images/0604/2487/1e18f.png)
![=\$ \{5000(1-\frac1{10})\}(1-\frac1{10})](/tpl/images/0604/2487/4abb3.png)
![=\$ \{5000(1-\frac1{10})^2\}](/tpl/images/0604/2487/42964.png)
Similarly the value of car after t years is
![=\$ \{5000(1-\frac1{10})^t\}](/tpl/images/0604/2487/62704.png)
The function that gives the car's value is
![V(t)=5000(1-\frac1{10})^t](/tpl/images/0604/2487/36d8c.png)
where V(t) is in dollar and t is number of years after it sold.