Question

a company currently has 500 employees. The number of employees is expected to grow by 10% each year. write an exponential function to model the number of employees in the company, y, after x years.
y=_____
what is the y-intercept of this function? (enter only the y-coordinate only. Do NOT enter your answer in ordered pair form)

Answer 1

To model the number of employees in the company, we can use the exponential function:

\[
y = 500(1 + r)^x
\]
where \(r\) is the growth rate (10% or 0.10), so:

\[
y = 500(1 + 0.10)^x
\]
\[
y = 500(1.10)^x
\]

Now, we can determine the y-intercept of this function. The y-intercept occurs when \(x = 0\):

\[
y = 500(1.10)^0
\]
Since \( (1.10)^0 = 1 \):

\[
y = 500 \cdot 1 = 500
\]

Thus, the y-intercept of this function is:

**500**