Exponential functions

[KG101]

I don't even know where to start. Any help would be great. Thanks.

True or false: The function "f(x) = 3^x" grows three times faster than the function "g(x) = x". Explain.

 

[pka]

True or false: The function "f(x) = 3x" grows three times faster than the function "g(x) = x". Explain.

Can you tell us what you think the question means?

Have you looked at some values?
\(\displaystyle \begin{array}{rcl}
g(1) = 1\quad & \& & \quad f(1) = 3 \\
g(2) = 2\quad & \& & \quad f(2) = 6 \\
g(3) = 3\quad & \& & \quad f(3) = 9 \\
\end{array}\)

 

[soroban]

Hello, KG101!

True or false:
The function \(\displaystyle f(x) \:= \:3^x\) grows three times faster than the function \(\displaystyle g(x) \,=\,x\)

Now that the problem is edited and corrected,
. . I'll ask, too: "Have you looked at some values?"

\(\displaystyle \begin{array}{ccc}x & | & 0 & | & 1 & | & 2 & | & 3 & | & 4 & | & 5 & |\\ \hline \\
f(x)\,=\,e^x & | & 1 & | & 3 & | & 9 & | & 27 & | & 81 & | & 243 & |\\ \hline \\
g(x)\,=\,x & | & 0 & | & 1 & | & 2 & | & 3 & | & 4 & | & 5 & | \\ \hline\end{array}\)