Question

Compare the functions f(x) = 4* and g(x)= 225x by completing parts (a) and (b).(a) Fill in the table below. Note that the table is already filled in for X = 3.(b) For X24, the table suggesks that f (x) is(Choose one)greater than g (x)

Answer 1

(a)

x f(x) g(x)

3 64 675

4 256 900

5 1024 1125

6 4096 1350

7 16384 1575

Step-by-step explanation:

To complete the table, we need to replace the value of x on each equation. So, for each x, we get

`\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}`
`\begin{gathered} \text{ For x = 5} \\ f(4)=4^5=1024 \\ g(5)=225(5)=1125 \end{gathered}`
`\begin{gathered} \text{ For x = 6} \\ f(6)=4^6=4096 \\ g(6)=225(6)=1350 \end{gathered}`
`\begin{gathered} \text{ For x = 7} \\ f(7)=4^7=16384 \\ g(7)=225(7)=1575 \end{gathered}`

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).