5. The value of four functions for different values of x are shown in the table above. If the patterns continue, which function will have the largest value when x is equal to 100,000?
Answer: C
C(x) will have the largest value when x is equal to 100,000.
Based on the patterns observed in the functions provided in the table, C(x) demonstrates the most rapid increase in value as x approaches 100,000.
A) A(x)
A(x) shows a slower growth rate compared to the other functions. While it does increase with x, its rate of increase is not sufficient to reach the highest value when x is 100,000.
B) B(x)
B(x) has a moderate growth pattern, but it does not keep pace with the exponential increase exhibited by C(x). As a result, it will not achieve the largest value at x = 100,000.
C) C(x)
C(x) exhibits the fastest growth rate among the functions provided. Its pattern indicates that as x increases, C(x) will surpass the values of the other functions substantially when x is equal to 100,000.
D) D(x)
D(x) has a growth pattern that is less aggressive than that of C(x). While it does increase, it does not reach the same magnitude of values as C(x) by the time x is 100,000.
Conclusion
C(x) stands out as the function with the highest value at x = 100,000 due to its rapid growth trend. The other options, A(x), B(x), and D(x), do not exhibit the same level of increase, thereby confirming C(x) as the correct choice based on the observed patterns.