Question the-fu
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 ?
0.04
0.4
1.04
1.4
The function S above models the annual salary, in dollars, of an employee n years after
Hard-difficulty · SAT Math · Nonlinear Functions — Exponential growth and decay functions. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.
Answer explanation
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’s given that the annual increase in an employee’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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