Given:
[tex]\begin{gathered} f(x)=3^x \\ g(x)=45x^2 \end{gathered}[/tex]
Required:
To fill the given table.
Explanation:
When x=5,
[tex]\begin{gathered} f(5)=3^5 \\ =243 \\ g(5)=45(5)^2 \\ =1125 \end{gathered}[/tex]
When x=7,
[tex]\begin{gathered} f(7)=3^7 \\ =2187 \\ g(7)=45(7)^2 \\ =2205 \end{gathered}[/tex]
When x=8,
[tex]\begin{gathered} f(8)=3^8 \\ =6561 \\ g(8)=45(8)^2 \\ =2880 \end{gathered}[/tex]
When x=9,
[tex]\begin{gathered} f(9)=3^9 \\ =19683 \\ g(9)=45(9)^2 \\ =3645 \end{gathered}[/tex]
(b) For x>=8 the f(x) value is always greater than g(x).
Final Answer:
(a)
The complete table is
x f(x) g(x)
5 243 1125
7 2187 2205
8 6561 2880
9 19683 3645
(b) For x>=8 the f(x) value is always greater than g(x).
