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Students in a statistics class examined individual student test scores for a large group of students. Each test score is paired with the reported time the student spent studying. The class observed that when study time doubled, test scores generally increased by points. For example, a student who studied minutes generally scored points higher than a student who studied minutes. For nonzero constants and , which of the following types of functions is most useful in modeling test scores as a function of time studied, in minutes?

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Honormao2219
The description of the relationship between study time and test scores, where doubling study time generally leads to an increase in test scores, suggests an exponential function. Exponential functions have the form \(f(x) = a \cdot b^x\), where \(a\) and \(b\) are constants.

In this case, since doubling study time results in an increase in test scores, it aligns with the behavior of exponential growth. Therefore, an exponential growth function \(f(x) = a \cdot 2^x\) could be a suitable model for test scores as a function of time studied.

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