Question

complete the table of values for $f(x) = x^2 + 7$ and $g(x) = 3(2)^x$.

$x$	$f(x)$	$g(x)$
1
2
3

both $f(x)$ and $g(x)$ grow as $x$ gets larger and larger. which function eventually exceeds the other?
$f(x) = x^2 + 7$ $g(x) = 3(2)^x$

Explanation:

Step1: Calculate f(0)

$f(0) = 0^2 + 7 = 7$

Step2: Calculate g(0)

$g(0) = 3(2)^0 = 3\times1 = 3$

Step3: Calculate f(1)

$f(1) = 1^2 + 7 = 1 + 7 = 8$

Step4: Calculate g(1)

$g(1) = 3(2)^1 = 3\times2 = 6$

Step5: Calculate f(2)

$f(2) = 2^2 + 7 = 4 + 7 = 11$

Step6: Calculate g(2)

$g(2) = 3(2)^2 = 3\times4 = 12$

Step7: Calculate f(3)

$f(3) = 3^2 + 7 = 9 + 7 = 16$

Step8: Calculate g(3)

$g(3) = 3(2)^3 = 3\times8 = 24$

Step9: Compare long-term growth

Exponential functions outpace quadratic functions as $x\to\infty$.

Answer:

Completed Table:

$x$	$f(x)$	$g(x)$
1	8	6
2	11	12
3	16	24

Growth Comparison Answer:

$g(x) = 3(2)^x$