Question

Compare the functions f(x) = 2 and g(x) = 150x by completing parts (a) and (b). (a) Fill in the table below. Note that the table is already filled in for X=5. ) (b) For x 211, the table suggests that f (x)is (Choose one) greater than g(x).

Answer 1

Evaluate the functions f and g at x=6,10,11 and 12 to find the missing values of the table:

$\begin{gathered} f(x)=2^x \\ \\ \Rightarrow f(6)=2^6=64 \\ \Rightarrow f(10)=2^{10}=1024 \\ \Rightarrow f(11)=2^{11}=2048 \\ \Rightarrow f(12)=2^{12}=4096 \end{gathered}$$\begin{gathered} g(x)=150x \\ \\ \Rightarrow g(6)=150\times6=900 \\ \Rightarrow g(10)=150\times10=1500 \\ \Rightarrow g(11)=150\times11=1650 \\ \Rightarrow g(12)=150\times12=1800 \end{gathered}$

As we can see, f(11) is greater than g(11), and the values of f(12) and g(12) suggest that this behavior continues for all x greater than 11.

Then, for x≥11, the table suggest that f(x) is always greater than g(x).