Fabulous Fabrics is a new clothing brand that is growing fast. The company currently employs a team of 33 people and plans to increase that by about \( \frac{1}{3} \) each ycor while continuing to expand. Write an exponential equation in the form \( y=a(b)^{x} \) that can model the number of employees, \( y \), in \( x \) years. Use whole numbers, decimals, or simplified froctions for the values of a and \( b \). \[ y=\square \text { To the nearest whole number, how many employces does the company expect to have after } 4 \] years? employees

**Step 1: Identify the initial value and growth factor** The company starts with 33 employees. Since the number of employees increases by \( \frac{1}{3} \) (which is approximately 33.33%) each year, the growth factor is: \[ 1 + \frac{1}{3} = \frac{4}{3} \] **Step 2: Write the exponential equation** The exponential growth model has the form \[ y = a(b)^x \] where \( a \) is the initial number of employees and \( b \) is the growth factor. Substituting the values, we get: \[ y = 33\left(\frac{4}{3}\right)^x \] **Step 3: Calculate the number of employees after 4 years** Replace \( x \) with 4 in the equation: \[ y = 33\left(\frac{4}{3}\right)^4 \] **Step 4: Compute \(\left(\frac{4}{3}\right)^4\)** First, compute the numerator and denominator separately: \[ \left(\frac{4}{3}\right)^4 = \frac{4^4}{3^4} = \frac{256}{81} \] **Step 5: Multiply by 33 and simplify** The number of employees after 4 years is: \[ y = 33 \times \frac{256}{81} = \frac{8448}{81} \approx 104.44 \] **Step 6: Round to the nearest whole number** Rounding \( 104.44 \) to the nearest whole number, we get: \[ 104 \] Thus, the exponential equation modeling the number of employees is: \[ y = 33\left(\frac{4}{3}\right)^x \] And the company expects to have approximately 104 employees after 4 years.