To find the value of $e^{-1.17}$ using Gregory-Newton Forward Interpolation Formula, we need a table of function values at certain points. The Gregory-Newton Forward formula is generally used for evenly spaced data points. Here's the formula:

$f(x) = f(x_0) + u\Delta f(x_0) + \frac{u(u-1)}{2!}\Delta^2 f(x_0) + \frac{u(u-1)(u-2)}{3!}\Delta^3 f(x_0) + \ldots$

where:

• $u = \frac{x - x_0}{h}$
• $h$ is the step size between the data points
• $\Delta f(x_0), \Delta^2 f(x_0),$ etc., are forward differences.

To proceed with finding $e^{-1.17}$, please provide the table of values (e.g., values of $x$ and corresponding function values $f(x)$), or let me know if you need help creating one.

Would you like me to guide you through the process step-by-step if you provide the necessary data?

Related Questions

1. How do you calculate forward differences for interpolation?
2. What is the significance of the Gregory-Newton Forward Interpolation Formula?
3. How do you determine the step size $h$ in interpolation problems?
4. What are the applications of interpolation formulas in real-life scenarios?
5. Can backward interpolation be used similarly, and how does it differ?

Tip: Always ensure that the data points are evenly spaced when applying the Gregory-Newton Forward Interpolation Formula for accurate results.