complete the table of values for ( f(x)=3^{x} ) and ( g(x)=3x + 5 ).\n\nboth ( f(x) ) and ( g(x) ) grow as (…

Explanation:

Step1: Calculate (f(x)) and (g(x)) for (x = 1)

For (f(x)=3^{x}), when (x = 1), (f(1)=3^{1}=3). For (g(x)=3x + 5), when (x = 1), (g(1)=3\times1+5=3 + 5=8).

Step2: Calculate (f(x)) and (g(x)) for (x = 2)

For (f(x)=3^{x}), when (x = 2), (f(2)=3^{2}=9). For (g(x)=3x + 5), when (x = 2), (g(2)=3\times2+5=6 + 5=11).

Step3: Calculate (f(x)) and (g(x)) for (x = 3)

For (f(x)=3^{x}), when (x = 3), (f(3)=3^{3}=27). For (g(x)=3x + 5), when (x = 3), (g(3)=3\times3+5=9 + 5=14).

Step4: Calculate (f(x)) and (g(x)) for (x = 4)

For (f(x)=3^{x}), when (x = 4), (f(4)=3^{4}=81). For (g(x)=3x + 5), when (x = 4), (g(4)=3\times4+5=12 + 5=17).

Step5: Determine which function exceeds the other

An exponential function (y = a^{x}(a>1)) has a faster - growing rate than a linear function (y=mx + b(m>0)) as (x\to+\infty). Here (f(x)=3^{x}) is an exponential function ((a = 3>1)) and (g(x)=3x + 5) is a linear function ((m = 3>0)).

Answer:

(x)	(f(x))	(g(x))
(1)	(3)	(8)
(2)	(9)	(11)
(3)	(27)	(14)
(4)	(81)	(17)

The function (f(x)=3^{x}) eventually exceeds the other function.