Question

Two students were asked to find the value of a $1000 item after 3 years. The item was depreciating (losing value) at a rate of 40% per year. Which is incorrect? Explain the error. Student 1: `1000(0.6)^{3}=$216` Student 2: `1000(0.4\right)^{3}=\$64`

Answer 1

Student 2 is incorrect because he didn't use the formula properly

Explanation:

The exponential function is often used to model natural growing or decaying processes, where the change is proportional to the actual quantity.

An exponential decaying function is expressed as:

`C(t)=C_o\cdot(1-r)^t`

Where:

C(t) is the actual value of the function at time t

Co is the initial value of C at t=0

r is the decaying rate, expressed in decimal

The initial value of the item is Co=$1000, the rate of decay is r=40%=0.4, and the time is t=3 years.

Substituting into the formula:

`C(3)=\$1000\cdot(1-0.4)^3`

`C(3)=\$1000\cdot0.6^3`

C(3)=$216

Student 2 is incorrect because he didn't use the formula properly