Using an exponential function, it is found that f(5.5) = 19.8.
An exponential function is a function in which the growth rate is a percentage, modeled by:
[tex]y = ab^x[/tex]
In which:
f(3.5) = 25 means that:
[tex]ab^{3.5} = 25[/tex]
[tex]a = \frac{25}{b^{3.5}}[/tex]
f(8.5) = 14 means that:
[tex]ab^{8.5} = 14[/tex]
Hence:
[tex]\frac{25}{b^{3.5}} \times b^{8.5} = 14[/tex]
[tex]25b^5 = 14[/tex]
[tex]b = \sqrt[5]{\frac{14}{25}}[/tex]
[tex]b = 0.89[/tex]
[tex]a = \frac{25}{0.89^{3.5}} = 37.59[/tex]
Hence, the function is given by:
[tex]y = 37.59(0.89)^x[/tex]
Then, when x = 5.5:
[tex]f(5.5) = 37.59(0.89)^{5.5} = 19.8[/tex]
More can be learned about exponential functions at https://brainly.com/question/25537936
