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Te’Andra has a computer system that she bought for $5000. Each year, the computer system loses one-fifth of its then-current value. How much money will the computer system be worth after 6 years? Round to the nearest cent.

TeAndra has a computer system that she bought for 5000 Each year the computer system loses onefifth of its thencurrent value How much money will the computer sy class=

Respuesta :

Answer:

$1310.72

Explanation:

The value of its computer after one year will be equal to

$5000 - (1/5)$5000

= $5000(1 - 1/5)

= $4000

Because it loses one-fift of its current value, then the second year will be

= $4000 - (1/5)$4000

= $4000( 1 - 1/5)

= $5000( 1 - 1/5)(1 - 1/5)

= $5000(1 - 1/5)²

Then, after year n, the value of the computer will be

= $5000( 1 - 1/5)ⁿ

Replacing n by 6, we get:

= $5000( 1 - 1/5)⁶

= $1310.72

Therefore, the answer is

$1310.72