compare the functions f(x)=45x² and g(x)=4^x by completing parts (a) and (b). (a) fill in the table below…
compare the functions f(x)=45x² 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)=45x² g(x)=4^x 3 405 64 4 5 6 7 (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 $f(4)$
Substitute $x = 4$ into $f(x)=45x^{2}$. So $f(4)=45\times4^{2}=45\times16 = 720$.
Step2: Calculate $g(4)$
Substitute $x = 4$ into $g(x)=4^{x}$. So $g(4)=4^{4}=256$.
Step3: Calculate $f(5)$
Substitute $x = 5$ into $f(x)=45x^{2}$. So $f(5)=45\times5^{2}=45\times25 = 1125$.
Step4: Calculate $g(5)$
Substitute $x = 5$ into $g(x)=4^{x}$. So $g(5)=4^{5}=1024$.
Step5: Calculate $f(6)$
Substitute $x = 6$ into $f(x)=45x^{2}$. So $f(6)=45\times6^{2}=45\times36 = 1620$.
Step6: Calculate $g(6)$
Substitute $x = 6$ into $g(x)=4^{x}$. So $g(6)=4^{6}=4096$.
Step7: Calculate $f(7)$
Substitute $x = 7$ into $f(x)=45x^{2}$. So $f(7)=45\times7^{2}=45\times49 = 2205$.
Step8: Calculate $g(7)$
Substitute $x = 7$ into $g(x)=4^{x}$. So $g(7)=4^{7}=16384$.
Answer:
| $x$ | $f(x)=45x^{2}$ | $g(x)=4^{x}$ |
|---|---|---|
| $4$ | $720$ | $256$ |
| $5$ | $1125$ | $1024$ |
| $6$ | $1620$ | $4096$ |
| $7$ | $2205$ | $16384$ |
| (b) always |