An exponential equation is characterized by an initial value "a" and a rate "b". Because Jerald is investigating a depreciation, the rate "b" will be less than 1.
The exponential equation is [tex]y = 12500(0.86)^x[/tex] and the depreciated amount in 2010 is approximately 2379
I've added the missing data as an attachment.
An exponential equation is represented as:
[tex]y = ab^x[/tex]
Where:
[tex]a \to[/tex] the first term
[tex]b \to[/tex] rate
[tex]x \to[/tex] years after 1999
[tex]y \to[/tex] depreciated value
When [tex]x = 0\ \&\ y=12500[/tex]
The equation [tex]y = ab^x[/tex] is:
[tex]12500 = ab^0[/tex]
[tex]12500 = a*1[/tex]
[tex]12500 = a[/tex]
[tex]a =12500[/tex]
When [tex]x = 1\, \&\ y = 10750[/tex]
The equation [tex]y = ab^x[/tex] is:
[tex]10750 = ab^1[/tex]
[tex]10750 = ab[/tex]
Substitute [tex]a =12500[/tex]
[tex]10750 = 12500 \times b[/tex]
Solve for b
[tex]b =\frac{10750 }{12500}[/tex]
[tex]b =0.86[/tex]
So, the equation is:
[tex]y = ab^x[/tex]
[tex]y = 12500(0.86)^x[/tex]
To calculate the depreciated value in 2010, we first solve for x in 2010
[tex]x = 2010 - 1999[/tex]
[tex]x = 11[/tex]
So, the depreciated value (y) is:
[tex]y = 12500(0.86)^x[/tex]
[tex]y = 12500 \times 0.86^{11}[/tex]
[tex]y = 2379[/tex]
Read more about exponential equation at:
https://brainly.com/question/17161065
