Answer:
[tex]f(2) = 12[/tex]
[tex]f(5) =320[/tex]
[tex]f(-2) =\frac{5}{2}[/tex]
[tex]g(3) = \frac{1}{135}[/tex]
Step-by-step explanation:
Solving (1):
[tex]f(x) = \frac{1}{3}*6^x[/tex] at [tex]x=2[/tex]
Substitute 2 for x in f(x)
[tex]f(2) = \frac{1}{3}*6^2[/tex]
[tex]f(2) = \frac{1}{3}*36[/tex]
[tex]f(2) = \frac{1*36}{3}[/tex]
[tex]f(2) = \frac{36}{3}[/tex]
[tex]f(2) = 12[/tex]
Solving (2):
[tex]f(n) =10*2^n[/tex] at [tex]n =5[/tex]
Substitute 5 for n in f(n)
[tex]f(5) =10*2^5[/tex]
[tex]f(5) =10*32[/tex]
[tex]f(5) =320[/tex]
Solving (3):
[tex]f(n) =10*2^n[/tex] at [tex]n =-2[/tex]
Substitute -2 for n in f(n)
[tex]f(-2) =10*2^{-2[/tex]
[tex]f(-2) =10*\frac{1}{2^2}[/tex]
[tex]f(-2) =10*\frac{1}{4}[/tex]
[tex]f(-2) =\frac{10*1}{4}[/tex]
[tex]f(-2) =\frac{10}{4}[/tex]
[tex]f(-2) =\frac{5}{2}[/tex]
Solving (4):
[tex]g(x) = \frac{1}{5}*(\frac{1}{3})^x[/tex] at [tex]x = 3[/tex]
Substitute 3 for x in g(x)
[tex]g(3) = \frac{1}{5}*(\frac{1}{3})^3[/tex]
[tex]g(3) = \frac{1}{5}*(\frac{1^3}{3^3})[/tex]
[tex]g(3) = \frac{1}{5}*\frac{1}{27}[/tex]
[tex]g(3) = \frac{1}{135}[/tex]
Solving (5):
Graph of [tex]f(x) = 4 * 2^x[/tex]
First, we determine the points to plot the graph.
When [tex]x = 0;\ f(0) = 4 * 2^0 = 4*1 = 4[/tex]
When [tex]x = 2;\ f(2) = 4 * 2^2 = 4*2 = 16[/tex]
When [tex]x = 4;\ f(4) = 4 * 2^4 = 4*16 = 64[/tex]
So, we have: (0,4), (2,16) and (4,16)
See attachment 1 for graph
Solving (6):
Graph of [tex]f(x) = 4 * (\frac{1}{2})^x[/tex]
First, we determine the points to plot the graph.
When [tex]x = 0;\ f(0) = 4 * (\frac{1}{2})^0 = 4*1 = 4[/tex]
When [tex]x = 2;\ f(2) = 4 * (\frac{1}{2})^2 = 4*\frac{1}{4} = 1[/tex]
When [tex]x = 4;\ f(4) = 4 * (\frac{1}{2})^4 = 4*\frac{1}{16} = \frac{1}{4}[/tex]
So, we have: (0,4), (2,1) and (4,1/4)
See attachment 2 for graph
