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Sagot :
A function that depicts depreciation can be represented as equations, graphs and tables.
The yearly value of each car for the first five years
The functions are given as:
[tex]V(t) =C(1 - r^t)[/tex]
[tex]V(t) =C(1 - r)^t[/tex]
Where:
C = 5895 --- the initial value of the car
r = 22% --- the rate of depreciation
For the first 5 years, the values of t = 1, 2, 3, 4 and 5
For the first function, we have:
[tex]V(1) =5895(1 - 22\%^1) = 4598.1[/tex]
[tex]V(2) =5895(1 - 22\%^2) = 5609.7[/tex]
[tex]V(3) =5895(1 - 22\%^3) = 5832.2[/tex]
[tex]V(4) =5895(1 - 22\%^4) = 5881.2[/tex]
[tex]V(5) =5895(1 - 22\%^5) = 5892.0[/tex]
For the second function, we have
[tex]V(1) =5895(1 - 22\%)^1 = 4598.1[/tex]
[tex]V(2) =5895(1 - 22\%)^2 = 3586.5[/tex]
[tex]V(3) =5895(1 - 22\%)^3 = 2797.5[/tex]
[tex]V(4) =5895(1 - 22\%)^4 =2182.0[/tex]
[tex]V(5) =5895(1 - 22\%)^5 = 1702.0[/tex]
So, the table of values is:
[tex]\left[\begin{array}{ccc}Years&Car\ 1&Car\ 2\\1&4598.1&4598.1\\2&5609.7&3586.5\\3&5832.2&2797.5\\4&5881.2&2182.0\\5&5892.0&1702.0\end{array}\right][/tex]
See attachment for the graphs of the two functions
Interpreting the graphs
The graph of car 1 increases up to C(t) = 5895, and then remains constant as the value of t increases while the graph of car 2 follows an exponential pattern.
This means that, the graph 2 that follows an exponential pattern is more realistic
The worth of the cars after 5 years
From the table, the worth of car 1 is $5892.0, while the worth of car 1 is $1702.0
Read more about graphs and functions at:
https://brainly.com/question/13473114
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