compare the functions f(x)=2^x and g(x)=4x^3 by completing parts (a) and (b). (a) fill in the table below…

compare the functions f(x)=2^x and g(x)=4x^3 by completing parts (a) and (b). (a) fill in the table below. note that the table is already filled in for x = 5. (the aleks calculator can be used to make computations easier.) x f(x)=2^x g(x)=4x^3 5 32 500 6 13 14 15 (b) for x≥6, the table suggests that f(x) is (choose one) less than g(x). (choose one) always sometimes never

compare the functions f(x)=2^x and g(x)=4x^3 by completing parts (a) and (b). (a) fill in the table below. note that the table is already filled in for x = 5. (the aleks calculator can be used to make computations easier.) x f(x)=2^x g(x)=4x^3 5 32 500 6 13 14 15 (b) for x≥6, the table suggests that f(x) is (choose one) less than g(x). (choose one) always sometimes never

Answer

Explanation:

Step1: Calculate $f(6)$

Substitute $x = 6$ into $f(x)=2^{x}$, so $f(6)=2^{6}=64$.

Step2: Calculate $g(6)$

Substitute $x = 6$ into $g(x)=4x^{3}$, so $g(6)=4\times6^{3}=4\times216 = 864$.

Step3: Calculate $f(13)$

Substitute $x = 13$ into $f(x)=2^{x}$, so $f(13)=2^{13}=8192$.

Step4: Calculate $g(13)$

Substitute $x = 13$ into $g(x)=4x^{3}$, so $g(13)=4\times13^{3}=4\times2197 = 8788$.

Step5: Calculate $f(14)$

Substitute $x = 14$ into $f(x)=2^{x}$, so $f(14)=2^{14}=16384$.

Step6: Calculate $g(14)$

Substitute $x = 14$ into $g(x)=4x^{3}$, so $g(14)=4\times14^{3}=4\times2744 = 10976$.

Step7: Calculate $f(15)$

Substitute $x = 15$ into $f(x)=2^{x}$, so $f(15)=2^{15}=32768$.

Step8: Calculate $g(15)$

Substitute $x = 15$ into $g(x)=4x^{3}$, so $g(15)=4\times15^{3}=4\times3375 = 13500$.

Step9: Analyze the relationship for $x\geq6$

By observing the values in the table for $x = 6,13,14,15$, we can see that sometimes $f(x)<g(x)$ and sometimes $f(x)>g(x)$.

Answer:

$x$ $f(x)=2^{x}$ $g(x)=4x^{3}$
6 64 864
13 8192 8788
14 16384 10976
15 32768 13500
(b) sometimes