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Nonlinear functions SAT question

Math · Advanced Math · Medium · Answer it here, explanation included.

$S of n, equals, 38,000 times a, to the n power$

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’s salary increases by 4% each year, what is the value of a ?

ExplanationShow

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 $S of n equals, I times, open parenthesis, 1 plus r over 100, close parenthesis, to the n power$ , where I is the initial value at time $n equals 0$ for r% annual increase. It’s given that the annual increase in an employee’s salary is 4%, so $r equals 4$ . The initial value can be found by substituting 0 for n in the given function, which yields $S of 0 equals 38,000$ . Therefore, $I equals 38,000$ . Substituting these values for r and I into the form of the exponential function $S of n equals, I times, open parenthesis, 1 plus r over 100, close parenthesis, to the n power$ yields $S of n equals, 38,000 times, open parenthesis, 1 plus 4 over 100, close parenthesis, to the n power$ , or $S of n equals, 38,000 times, 1 point 0 4 to the n power$ . 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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