The exponential decay formula is:
[tex]y=a(1-r)^x^{}[/tex]where y and x are the variables, a is the initial value, and r is the decay rate (as a decimal)
In the case of the values of a computer, the initial value is 960, that is, a = 960. y represents the value of the computer and x represents time. Substituting with x = 1, y = 720, and a = 960, we wet:
[tex]\begin{gathered} 720=960\cdot(1-r)^1 \\ \frac{720}{960}=1-r \\ 0.75=1-r \\ r=1-0.75 \\ r=0.25 \end{gathered}[/tex]Now we can check if this model predicts correctly the other values of the table.
[tex]\begin{gathered} y=960(1-0.25)^2=540 \\ y=960(1-0.25)^3=405 \end{gathered}[/tex]These results show that the value of the computer decay by a constant percentage rate per year.
The equation is:
[tex]y=960(1-0.25)^x=960(0.75)^x[/tex]