Applying the exponential function, it is found that the value of a is 0.1 = 10%.
The exponential equation for a depreciating value is given by:
[tex]V(t) = V(0)(1 - r)^t[/tex]
In which:
- V(0) is the initial value.
- r is the decay rate.
In this problem:
- Initial value of 60000, thus [tex]V(0) = 60000[/tex]
- Depreciates a% each year, thus [tex]r = a[/tex].
- In 2011, which is 6 years after 2005, value of 31886.46, thus [tex]V(6) = 31886.46[/tex]. This is used to find a.
[tex]V(t) = V(0)(1 - r)^t[/tex]
[tex]31886.46 = 60000(1 - a)^6[/tex]
[tex](1 - a)^6 = \frac{31886.46}{60000}[/tex]
[tex]\sqrt[6]{(1 - a)^6} = \sqrt[6]{\frac{31886.46}{60000}}[/tex]
[tex]1 - a = (\frac{31886.46}{60000})^{\frac{1}{6}}[/tex]
[tex]1 - a = 0.9[/tex]
[tex]a = 0.1[/tex]
Thus, a = 0.1 = 10%.
A similar problem is given at https://brainly.com/question/16201003
