Question

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Answer 1

Using an exponential function, it is found that f(5.5) = 19.8.

What is an exponential function?

An exponential function is a function in which the growth rate is a percentage, modeled by:

$y = ab^x$

In which:

• a is the initial value.

• b is the rate of change.

f(3.5) = 25 means that:

$ab^{3.5} = 25$

$a = \frac{25}{b^{3.5}}$

f(8.5) = 14 means that:

$ab^{8.5} = 14$

Hence:

$\frac{25}{b^{3.5}} \times b^{8.5} = 14$

$25b^5 = 14$

$b = \sqrt[5]{\frac{14}{25}}$

$b = 0.89$

$a = \frac{25}{0.89^{3.5}} = 37.59$

Hence, the function is given by:

$y = 37.59(0.89)^x$

Then, when x = 5.5:

$f(5.5) = 37.59(0.89)^{5.5} = 19.8$

More can be learned about exponential functions at brainly.com/question/25537936