A computer valued at $1500 loses 20% of its value each year.

a) write a function rule that models the value of the computer.

b) find he value of the computer after 3 years.

c) In how many years will the value of the computer be less then $500

A) The answer is F (n) = 1500 * 0.8ⁿ

Let the function be F (n) where n is number of years

After 20% is lost, the value that remains is 80% of 1500:

1500 : 100%

x : 80%

1500 : 100% = x : 80%

x = 1500 * 80% : 100%

x = 1500 * 80/100

x = 1500 * 0.8

For each year we must add exponent, so the function is:

F (n) = 1500 * 0.8ⁿ

b) The answer is $768

We have function: F (n) = 1500 * 0.8ⁿ

And we know that the number of years is 3: n = 3

F (3) = 1500 * 0.8³ = 1500 * 0.512 = 768

c) The answer is 5 years

We have function: F (n) = 1500 * 0.8ⁿ

And we know that the value needs to be less then $500: F (n) = <500

1500 * 0.8ⁿ < 500

0.8ⁿ < 500 / 1500

0.8ⁿ < 0.33

log (0.8ⁿ) < log (0.33)

n * log (0.8) < log (0.33)

n * - 0.0969 < - 0.4815

n < - 0.4815 / - 0.0969

n < 5