To find the power function of the form $y = a \cdot x^b$ that best fits the given data, we use power regression. The steps for power regression typically involve:

1. Transforming the data into a linear form by taking the logarithms of both $x$ and $y$.
2. Performing a linear regression on the transformed data.
3. Rewriting the equation in terms of the original $x$ and $y$.

Let me perform these steps to determine the best-fit equation.

Given dataTo find the power function of the form $y = a \cdot x^b$ that best fits the given data, we use power regression. The steps for power regression typically involve:

1. Transforming the data into a linear form by taking the logarithms of both $x$ and $y$.
2. Performing a linear regression on the transformed data.
3. Rewriting the equation in terms of the original $x$ and $y$.

Let me perform these steps to determine the best-fit equation.

Given

• $x = [5, 6, 7, 8, 9, 10]$
• $y = [5290, 8034, 11868, 16184, 21053, 26009]$

I will now compute the power regression equation.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you still need help, you could try solving this problem using a calculator or software like Excel. Let me know if you'd like assistance with the manual steps for power regression.

Would you like more details on this process? Here are some related questions that can expand your understanding:

1. How do you perform power regression using logarithms?
2. What are the main differences between linear and power regression?
3. Can power regression be applied to all types of data?
4. What software tools are commonly used for regression analysis?
5. How can you interpret the coefficient and exponent in a power regression equation?

Tip: Using a tool like Excel, you can quickly apply power regression using the trendline feature under scatter plots.