Neither Student 1's nor Student 2's function accurately represents the accumulated rainfall after h hours for Student 1's data. Student 1's function consistently underestimates the rainfall, while Student 2's function deviates from the actual rainfall amounts.
To determine whether the functions R(h) accurately represent the accumulated rainfall after h hours, consider the following criteria:
Input Validation: The function should be able to accept an integer value for h, representing the number of hours since the start of rainfall measurement.
Non-negative Output: The function's output, representing the accumulated rainfall, should be a non-negative number.
Data Consistency: The function's output should match the observed rainfall data for each corresponding hour.
Based on these criteria, let's analyze each function:
Student 1's Rainfall Function: R(h) = 0.2 * h
Input Validation: The function accepts an integer value for h.
Non-negative Output: The function always produces a non-negative output since h is multiplied by a positive constant.
Data Consistency: The function's output does not match the observed
rainfall data for Student 1. For instance, after 2 hours, the function predicts 0.4 inches of rainfall, while the actual rainfall is 0.3 inches.
Student 2's Rainfall Function: R(h) = 0.1 * h + 0.1
Input Validation: The function accepts an integer value for h.
Non-negative Output: The function always produces a non-negative output since 0.1h is always non-negative and adding a positive constant (0.1) further ensures a non-negative result.
Data Consistency: The function's output does not match the observed rainfall data for Student 1. For instance, after 3 hours, the function predicts 0.4 inches of rainfall, while the actual rainfall is 0.6 inches.