Answer:
The function that gives the car's value is
[tex]V(t)=5000(1-\frac1{10})^t[/tex]
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 [tex]\frac1{10}[/tex] of its value each year.
The value of car will loss after 1 year is
[tex]=\$5000 \times \frac1{10}[/tex]
The price of the car after 1 year is
[tex]=\$(5000-5000\times \frac 1{10})[/tex]
[tex]=\$\{5000(1-\frac1{10})\}[/tex]
[tex]=\$\{5000(1-\frac1{10})^1\}[/tex]
The value car will loss in 2 year is
[tex]=\$\{5000(1-\frac1{10})\times \frac1{10}\}[/tex]
After 2nd year the car will be
[tex]=\$ \{5000(1-\frac1{10})\}-\{5000(1-\frac1{10})\times \frac1{10}\}[/tex]
[tex]=\$ \{5000(1-\frac1{10})\}(1-\frac1{10})[/tex]
[tex]=\$ \{5000(1-\frac1{10})^2\}[/tex]
Similarly the value of car after t years is
[tex]=\$ \{5000(1-\frac1{10})^t\}[/tex]
The function that gives the car's value is
[tex]V(t)=5000(1-\frac1{10})^t[/tex]
where V(t) is in dollar and t is number of years after it sold.
