Question

Compare the functions f(x)=3^x and g(x)=45x^2 by completing parts a and B (THIS IS ONE QUESTION)

Answer 1

Given:

`\begin{gathered} f(x)=3^x \\ g(x)=45x^2 \end{gathered}`

Required:

To fill the given table.

Step-by-step explanation:

When x=5,

`\begin{gathered} f(5)=3^5 \\ =243 \\ g(5)=45(5)^2 \\ =1125 \end{gathered}`

When x=7,

`\begin{gathered} f(7)=3^7 \\ =2187 \\ g(7)=45(7)^2 \\ =2205 \end{gathered}`

When x=8,

`\begin{gathered} f(8)=3^8 \\ =6561 \\ g(8)=45(8)^2 \\ =2880 \end{gathered}`

When x=9,

`\begin{gathered} f(9)=3^9 \\ =19683 \\ g(9)=45(9)^2 \\ =3645 \end{gathered}`

(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).