Question

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

Answer 1

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