Question

An employee's salary,
S
(
n
)
, in dollars, at a company is a function of the number of years,
n
, that the employee has worked at the company.

The relationship between
n
and
S
(
n
)
is shown in the table below.

Answer 1

The question is incomplete. Here is the complete question.

An employee's salary, S(n), in dollars, at a company is a function of the number of years, n, that the employee has worked at the company.

The relationship between n and S(n) is shown in the table below.

Which of the following equations represents an explicit formula for S(n)?

A. S(n) = 40,000(1.05)ⁿ

B. S(n) = 40,000 + 1.05n

C. S(n) = 40,000(1.05)ⁿ⁻¹

D. S(n) = 40,000 + 1.05(n-1)

Answer: A. S(n) = 40,000(1.05)ⁿ

Step-by-step explanation: The table shows an exponential function, which is, in general, is of the form:

$S(n)=S_{0}r^{n}$

where

S₀ is the initial value

r is the rate the salary grows

n is the years the employee worked

From the table, in the first year, an employee receives $40,000, so, that is the initial value.

The salary increases at a constant rate of 1.05 per year, as shown below:

$r=\frac{42,000}{40,000}=\frac{44,100}{42,000}=\frac{46,305}{44,100}$

r = 1.05

So, the rate the salary grows is r = 1.05 or 5%.

Therefore, the equation that shows an explicit formula for S(n) is $S(n)=40,000(1.05)^{n}$.