Un=0.5*1.2^n
Sketch this for n= (0,1,2,3,4,5)
How do you sketch this?
graph the values
Put values of n on the x axis
and Un = .5*1.2^n on the y axis
eg
( 0 , .5 )
( 1 , .6 )
( 2 , .72 ) etc
To sketch the given function, you need to plot the values of Un for the given range of n values.
Start by substituting each value of n (0, 1, 2, 3, 4, 5) into the equation Un = 0.5 * 1.2^n 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
Once you have calculated the values of Un for each n, plot them on a graph with n on the x-axis and Un on the y-axis. Connect the plotted points to form a line. Since the given equation is an exponential function with a positive base (1.2), the curve will increase steadily as n increases.
On the graph, you will have the following points:
(0, 0.5), (1, 0.6), (2, 0.72), (3, 0.864), (4, 1.0368), (5, 1.24416)
Connect these points, and you will have the sketch of the function Un = 0.5 * 1.2^n.