4)Un=0.5*1.2^n
Sketch this for n= (0,1,2,3,4,5)
How do you sketch this?
To sketch the equation Un = 0.5 * 1.2^n for various values of n, you need to follow these steps:
1. Choose the range of values for n that you want to plot on the x-axis. In this case, n = (0, 1, 2, 3, 4, 5).
2. Substitute each value of n into the equation to find the corresponding values of Un.
For n = 0:
U0 = 0.5 * 1.2^0 = 0.5 * 1 = 0.5
For n = 1:
U1 = 0.5 * 1.2^1 = 0.5 * 1.2 = 0.6
For n = 2:
U2 = 0.5 * 1.2^2 = 0.5 * 1.44 = 0.72
For n = 3:
U3 = 0.5 * 1.2^3 = 0.5 * 1.728 = 0.864
For n = 4:
U4 = 0.5 * 1.2^4 = 0.5 * 2.0736 = 1.0368
For n = 5:
U5 = 0.5 * 1.2^5 = 0.5 * 2.48832 = 1.24416
3. Plot each point (n, Un) on a graph with n on the x-axis and Un on the y-axis.
In this case, the points to be plotted are:
(0, 0.5), (1, 0.6), (2, 0.72), (3, 0.864), (4, 1.0368), and (5, 1.24416).
4. Connect the points with a smooth curve to visualize the overall shape of the graph.
Note that the graph will start at (0, 0.5) and increase exponentially as n increases since the coefficient 1.2 is greater than 1.