compare the functions f(x)=2x^4 and g(x)=4^x by completing parts (a) and (b). (a) fill in the table below…
compare the functions f(x)=2x^4 and g(x)=4^x by completing parts (a) and (b). (a) fill in the table below. note that the table is already filled in for x = 3. (the aleks calculator can be used to make computations easier.) x f(x)=2x^4 g(x)=4^x 3 162 64 4 5 6 7 (b) for x≥4, the table suggests that f(x) is (choose one) less than g(x).
Answer
Explanation:
Step1: Calcular $f(x)$ para $x = 4$
Sustituir $x = 4$ en $f(x)=2x^{4}$. Entonces $f(4)=2\times4^{4}=2\times256 = 512$.
Step2: Calcular $g(x)$ para $x = 4$
Sustituir $x = 4$ en $g(x)=4^{x}$. Entonces $g(4)=4^{4}=256$.
Step3: Calcular $f(x)$ para $x = 5$
Sustituir $x = 5$ en $f(x)=2x^{4}$. Entonces $f(5)=2\times5^{4}=2\times625 = 1250$.
Step4: Calcular $g(x)$ para $x = 5$
Sustituir $x = 5$ en $g(x)=4^{x}$. Entonces $g(5)=4^{5}=1024$.
Step5: Calcular $f(x)$ para $x = 6$
Sustituir $x = 6$ en $f(x)=2x^{4}$. Entonces $f(6)=2\times6^{4}=2\times1296 = 2592$.
Step6: Calcular $g(x)$ para $x = 6$
Sustituir $x = 6$ en $g(x)=4^{x}$. Entonces $g(6)=4^{6}=4096$.
Step7: Calcular $f(x)$ para $x = 7$
Sustituir $x = 7$ en $f(x)=2x^{4}$. Entonces $f(7)=2\times7^{4}=2\times2401 = 4802$.
Step8: Calcular $g(x)$ para $x = 7$
Sustituir $x = 7$ en $g(x)=4^{x}$. Entonces $g(7)=4^{7}=16384$.
Answer:
| $x$ | $f(x)=2x^{4}$ | $g(x)=4^{x}$ |
|---|---|---|
| 4 | 512 | 256 |
| 5 | 1250 | 1024 |
| 6 | 2592 | 4096 |
| 7 | 4802 | 16384 |