The function S above models the annual salary, in dollars, of an employee n years after starting a job, where

Question

The function S above models the annual salary, in dollars, of an employee n years after starting a job, where a is a constant. If the employee&rsquo;s salary increases by 4% each year, what is the value of a ?

Accepted Answer

Choice C is correct. A model for a quantity S that increases by a certain percentage per time period n is an exponential function in the form , where I is the initial value at time for r % annual increase. It&rsquo;s given that the annual increase in an employee&rsquo;s salary is 4%, so . The initial value can be found by substituting 0 for n in the given function, which yields . Therefore, . Substituting these values for r and I into the form of the exponential function yields , or . Therefore, the value of a in the given function is 1.04. Choices A, B, and D are incorrect and may result from incorrectly representing the annual increase in the exponential function.

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