Question

A car sells for \$5000$5000dollar sign, 5000 and loses \dfrac{1}{10}

10

1

​

start fraction, 1, divided by, 10, end fraction of its value each year.

Write a function that gives the car's value, V(t)V(t)V, left parenthesis, t, right parenthesis, ttt years after it is sold.

Answer 1

The function that gives the car's value is

`V(t)=5000(1-\frac1{10})^t`

where V(t) is in dollar and t is number of years after it sold.

Explanation:

Given that,

A car sells for $5000 and losses
`\frac1{10}` of its value each year.

The value of car will loss after 1 year is

`=\$5000 * \frac1{10}`

The price of the car after 1 year is

`=\$(5000-5000* \frac 1{10})`

`=\$\{5000(1-\frac1{10})\}`

`=\$\{5000(1-\frac1{10})^1\}`

The value car will loss in 2 year is

`=\$\{5000(1-\frac1{10})* \frac1{10}\}`

After 2nd year the car will be

`=\$ \{5000(1-\frac1{10})\}-\{5000(1-\frac1{10})* \frac1{10}\}`

`=\$ \{5000(1-\frac1{10})\}(1-\frac1{10})`

`=\$ \{5000(1-\frac1{10})^2\}`

Similarly the value of car after t years is

`=\$ \{5000(1-\frac1{10})^t\}`

The function that gives the car's value is

`V(t)=5000(1-\frac1{10})^t`

where V(t) is in dollar and t is number of years after it sold.