Question

create a y vector such that y = ex where x = 1,2,3,4,5,6,7,8,9. plot the result on an xy graph. label the x - and y - axes and place a title on the graph.

Explanation:

Step1: Calculate y - values

Given $x = [1,2,3,4,5,6,7,8,9]$, and $y = ex$. We know that $e\approx2.71828$. So we calculate $y$ for each element in $x$ as follows:
For $x_1 = 1$, $y_1=e\times1\approx2.71828$; for $x_2 = 2$, $y_2=e\times2\approx2.71828\times2 = 5.43656$; for $x_3 = 3$, $y_3=e\times3\approx8.15484$; for $x_4 = 4$, $y_4=e\times4\approx10.87312$; for $x_5 = 5$, $y_5=e\times5\approx13.5914$; for $x_6 = 6$, $y_6=e\times6\approx16.30968$; for $x_7 = 7$, $y_7=e\times7\approx19.02796$; for $x_8 = 8$, $y_8=e\times8\approx21.74624$; for $x_9 = 9$, $y_9=e\times9\approx24.46452$. So $y=[2.71828,5.43656,8.15484,10.87312,13.5914,16.30968,19.02796,21.74624,24.46452]$.

Step2: Plot the graph

We can use a graph - plotting software (e.g., Python's Matplotlib library). In Matplotlib, we can use the following code:

import matplotlib.pyplot as plt
import numpy as np
x = np.array([1,2,3,4,5,6,7,8,9])
y = np.exp(1)*x
plt.plot(x,y)
plt.xlabel('x - axis')
plt.ylabel('y - axis')
plt.title('Graph of y = ex')
plt.show()

This code first creates the $x$ and $y$ arrays, then uses the plot function to plot the data points, labels the $x$ and $y$ axes, gives a title to the graph, and finally shows the graph.

Answer:

The $y$ - vector is approximately $[2.71828,5.43656,8.15484,10.87312,13.5914,16.30968,19.02796,21.74624,24.46452]$, and the graph can be plotted as described above with labeled axes and a title.