To model the growth of the number of employees in a company using an exponential function, we can use the formula:
\[ y = y_0 \cdot (1 + r)^x \]
where:
- \( y \) is the number of employees after \( x \) years,
- \( y_0 \) is the initial number of employees,
- \( r \) is the growth rate (as a decimal),
- \( x \) is the number of years.
In your case:
- The initial number of employees (\( y_0 \)) is 500.
- The growth rate (\( r \)) is 10%, which is 0.10 in decimal form.
Plugging these values into the formula, we get:
\[ y = 500 \cdot (1 + 0.10)^x \]
This simplifies to:
\[ y = 500 \cdot (1.10)^x \]
Thus, the exponential function that models the number of employees in the company after \( x \) years is:
\[ y = 500 \cdot (1.10)^x \]