A computer is programmed to combine 60,000 points of data in such a way that with each iteration, there are half as many data points as before. The number of data points after any number of iterations, x, can be modeled with the following function.
Answer
A
Both the mathematical and reasonable ranges are limited to real numbers greater than 0 and less than or equal to 60,000.
B
Both the mathematical and reasonable ranges are limited to whole numbers greater than 0 and less than or equal to 60,000.
C
The mathematical range is all real numbers greater than 0. The reasonable range is all real numbers greater than 0 and less than or equal to 60,000.
D
The mathematical range is all real numbers greater than 0. The reasonable range is all whole numbers greater than 0 and less than or equal to 60,000.
Explanation
The function halves 60,000 each iteration, so its output is positive and approaches 0 without ever reaching it. Mathematically, the exponential function can therefore have any positive real value as an output. In context, a number of data points must be a whole number and cannot exceed the initial 60,000, so the reasonable range is whole numbers greater than 0 and at most 60,000. This matches choice D.
AI-written and checked against the verified answer.