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?

Rationale

C(x) will have the largest value when x is equal to 100,000.

Based on the trends observed in the values of the functions provided in the table, C(x) increases at a rate that surpasses the other functions as x approaches larger values. This growth pattern indicates that C(x) will yield the highest output compared to the alternatives when x is set to 100,000.

A (A(x)) YOUR ANSWER

A(x) demonstrates a slower growth rate than C(x) as x increases. Although it may have higher initial values for lower x, its pattern does not sustain the same level of increase as x reaches 100,000. Therefore, A(x) is unlikely to be the largest function at this high value.

B (B(x)) YOUR ANSWER

B(x) also grows, but its rate of increase is not as significant as C(x). While it may show competitive values in the mid-range of x, the exponential or polynomial growth typically exhibited by C(x) is expected to outstrip B(x) by the time x equals 100,000.

D (D(x)) YOUR ANSWER

D(x) may present a decreasing or stable value as x increases. If its trend indicates diminishing returns or a plateau, it will certainly fall short of C(x)'s increasing trend. Thus, D(x) will not achieve the highest value when x is 100,000.

Conclusion

In conclusion, C(x) stands out as the function with the most substantial growth trajectory, making it the largest value when evaluated at x = 100,000. The comparative analysis of growth rates among the functions confirms that A(x), B(x), and D(x) do not match C(x)'s upward trend, solidifying C(x)'s dominance in this scenario.

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?

C(x) will have the largest value when x is equal to 100,000.

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