A company paid $150 comma 000 for a new 18-wheeler. When it is 9 years old it will be worth $51 comma 000. Using straight-line depreciation, the value of the truck in dollars, V, is a linear function of its age in years, n. Find the function and the value when the truck is 8 years old

V = - 11,000n + $150,000; $62,000

Explanation:

Given that,

Cost of new 18-wheeler = $150,000

When it is 9 years old, worth = $51,000

Let the function be: V = xn + y

where,

x and y are constants.

V = value of the truck in dollars

n = age in years

When n = 0, V = $150,000

When n = 9, V = $51,000

According to the equation,

When n = 0, V = $150,000

$150,000 = x (0) + y

$150,000 = y

When n = 9, V = $51,000

V = xn + y

$51,000 = x (9) + $150,000

$51,000 - $150,000 = 9x

-$99,000 = 9x

-$11,000 = x

Function: V = - 11,000n + $150,000

Therefore,

When the truck is 8 years old, the value of truck is as follows:

= xn + y

= (-$11,000) (8) + $150,000

= - $88,000 + $150,000

= $62,000