Let's first calculate the values of
Calculating Values
-
For
: -
For
: -
For
: -
For
:
Filling the Table
Now we can complete the table:
Analyzing Growth of Functions
Next, we need to determine which function eventually exceeds the other as
is a linear function, growing at a constant rate of 3. is a quadratic function, which grows faster as increases because quadratic functions increase faster than linear functions for sufficiently large .
To find out when
Rearranging gives us:
Calculating the discriminant:
Since the discriminant is negative, this means the equation has no real solutions which indicates that
Conclusion
Thus, while both functions grow,