The cubic polynomial equation that fits the data is:

$y(t) = 25.28t^3 - 76.44t^2 + 51.28t + 16.21$

This equation provides a close approximation to the data points in the table.

Would you like to go into more detail about the method, or do you have any questions?

Here are some related questions:

1. How do we decide on the degree of the polynomial for fitting data?
2. What does each term in a polynomial represent in terms of the data trend?
3. How can we assess the accuracy of the fit?
4. Can we use other types of functions besides polynomials to fit the data?
5. How do we calculate the residuals (differences) between the observed data and the fitted values?

Tip: Higher-degree polynomials may fit data better but can also lead to overfitting, making the model less generalizable.