To determine whether the bonus increases for the two companies are best modeled by linear or nonlinear functions, let's analyze each company's description.
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Company 1: The bonus increases by a fixed dollar amount of $50 each year. This is a constant increase, which can be represented by a linear function. In mathematical terms, if \( B(t) \) is the bonus after \( t \) years, it would be \( B(t) = B_0 + 50t \), where \( B_0 \) is the starting bonus.
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Company 2: The bonus increases by 5% each year. This means that the increase is a percentage of the current bonus, leading to exponential growth. In this case, if the initial bonus is \( B_0 \), after \( t \) years the bonus would be \( B(t) = B_0(1 + 0.05)^t \). This is a classic example of exponential growth, which is nonlinear.
Based on this analysis:
- The description for Company 1 is best modeled by a linear function.
- The description for Company 2 is best modeled by a nonlinear function.
Thus, the correct statement is:
The description for Company 1 is best modeled by a linear function, while the description for Company 2 is best modeled by a nonlinear function.
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