Answer:
(a)
x f(x) g(x)
3 64 675
4 256 900
5 1024 1125
6 4096 1350
7 16384 1575
Explanation:
To complete the table, we need to replace the value of x on each equation. So, for each x, we get
[tex]\begin{gathered} \text{ For x = 4} \\ f(x)=4^x \\ f(4)=4^4=256 \\ \\ g(x)=225x \\ g(4)=225(4)=900 \end{gathered}[/tex][tex]\begin{gathered} \text{ For x = 5} \\ f(4)=4^5=1024 \\ g(5)=225(5)=1125 \end{gathered}[/tex][tex]\begin{gathered} \text{ For x = 6} \\ f(6)=4^6=4096 \\ g(6)=225(6)=1350 \end{gathered}[/tex][tex]\begin{gathered} \text{ For x = 7} \\ f(7)=4^7=16384 \\ g(7)=225(7)=1575 \end{gathered}[/tex]
Therefore, the complete table is
x f(x) g(x)
3 64 675
4 256 900
5 1024 1125
6 4096 1350
7 16384 1575
Now, we can see that f(x) is greater than g(x) when x is greater than 6 or 7, so for greater values, f(x) will be greater than g(x). However for x = 3, x = 4, and x = 5, f(x) is lower than g(x).
