Question

The value of a computer depreciates with age, as shown in the table.

Value of a Computer

A 2-column table with 5 rows. The first column is labeled age of computer (years) with entries 0, 1, 2, 3, 4. The second column is labeled value of computer (dollar sign) with entries 1,600.00; 1,280.00; 1,024.00; 819.20; 655.36.

Which function represents the value of a computer after t years?

f(t) = 1,600 – 226.16t
f(t) = 1,600 – 320t
f(t) = 1,600(0.2)t
f(t) = 1,600(0.8)t

Answer 1

f(t) = 1,600(0.8)^t

Each year the value is multiplied by 1280/1600 = 0.8, so the decay is exponential with factor 0.8 (1600·0.8 = 1280, 1600·0.8^2 = 1024, ...).