Next Generation ACCUPLACER Scores Quantitative Reasoning Algebra and Statistics

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Question 1

The table above shows some values for the function f. If f(x)=ka^x for some constants k and a, what is the value of a?

Your Answer: Option(s)

Correct Answer: Option(s) D

Rationale

The value of a is 4.

In the function f(x) = ka^x, the constant a determines the growth or decay rate of the exponential function. By analyzing the provided values in the table, we can deduce that the value of a that fits the exponential model is 4.

A) 12
This value suggests a decay factor, which would imply that the function decreases as x increases. However, given the values in the table, the function exhibits growth, indicating that a must be greater than 1 to produce increasing outputs. Therefore, 12 is not a suitable choice.

B) 14
Similar to 12, a value of 14 also indicates decay, leading to an exponential decrease as x increases. The table values do not support this since they reflect growth rather than decay. Hence, 14 cannot be the correct answer.

C) 2
While a value of 2 would still indicate growth, it does not align with the steepness of the increase observed in the table values. The function f(x) = k(2)^x would produce values that are lower than those indicated, suggesting that a must be greater than 2 to fit the observed growth pattern.

D) 4
This value signifies a rapid growth rate for the function f(x). When we apply a = 4 in the function, the resulting values match the exponential increase shown in the table. Thus, a value of 4 accurately represents the growth factor required for the function.

Conclusion
The analysis of the function f(x) = ka^x reveals that the only appropriate choice for a, based on the values provided in the table, is 4. This value supports the observed exponential growth, while all other options indicate decay or insufficient growth rates. Understanding the behavior of exponential functions is crucial for accurately interpreting their parameters.

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The value of a is 4.

(x^3-1)^2

sin 45 deg * cos 45 deg * tan 45 deg = 01-Feb.

4x² + 20xy + 25y² can be factored into the form (ax + by)².

The value of k that ensures the graph does not intersect the x-axis is 4.

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The value of a is 4.

(x^3-1)^2

sin 45 deg * cos 45 deg * tan 45 deg = 01-Feb.

4x² + 20xy + 25y² can be factored into the form (ax + by)².

The value of k that ensures the graph does not intersect the x-axis is 4.

Free Preview Ended

Unlock Full Access

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