To find the power function that best fits the given data, we can express the function in the form:

$y = a \cdot x^b$

where $a$ and $b$ are constants to be determined.

Steps:

1. Linearize the power function by taking the natural logarithm (ln) of both sides:

$\ln(y) = \ln(a) + b \cdot \ln(x)$

This equation is now in the form of a linear equation $y = mx + c$, where $\ln(y)$ corresponds to the dependent variable, $\ln(x)$ is the independent variable, $b$ is the slope, and $\ln(a)$ is the intercept.

2. Apply linear regression on the transformed data, where $\ln(y)$ is regressed on $\ln(x)$.

I will now calculate the best-fit values of $a$ and $b$ for the power function. Let me compute that for you.The power function that best fits the given data is:

$y = 3.00 \cdot x^{0.50}$

Would you like further details or clarification on how this was calculated?

Here are five related questions to explore further:

1. How does the natural logarithm help linearize non-linear equations like power functions?
2. Can the power function method be used for all types of data trends?
3. What is the significance of the coefficient $a$ in the power function?
4. How can we assess the goodness of fit for a power function?
5. What happens to the power function if $b$ is negative?

Tip: Always check the residuals of your regression to ensure the model fits well.