The function that best represents the value of the real estate after t years is: [tex]f(t) = 101234(1.03)^t[/tex]
The table is represented as:
Years - Values
1 - $104,271. 02
2 - $107,399. 15
Appreciation and depreciation are often represented using exponential function as follows:
[tex]f(x) = ab^x[/tex]
At year 1, we have:
[tex]104271. 02 = ab^1[/tex]
[tex]104271. 02 = ab[/tex]
At year 2, we have:
[tex]107399. 15 = ab^2[/tex]
Divide both equations
[tex]\frac{107399.15}{104271.02} = \frac{ab^2}{ab}[/tex]
[tex]1.03 = b[/tex]
Rewrite as:
[tex]b = 1.03[/tex]
He bought the real estate for $101,234.
So, we have:
[tex]a = 101234\\[/tex]
Substitute values for (a) and (b) in [tex]f(x) = ab^x[/tex]
[tex]f(x) = 101234(1.03)^x[/tex]
Replace x with t
[tex]f(t) = 101234(1.03)^t[/tex]
Hence. the function that best represents the value of the real estate after t years is: [tex]f(t) = 101234(1.03)^t[/tex]
Read more about exponential functions at:
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