The number of students enrolled at a college is 17,000 and grows $$ 3 \% $$ each year. Complete parts (a) through (e). c) To find the number of students enrolled after one year, you calculate $$ 17,000 \cdot 1.03 $$. d) Complete the equation $$ y=17,000 \cdot 1.03^{x} $$ to find the number of students enrolled after $$ x $$ years. e) Use your equation to predict the number of students enrolled after 22 years. Ater 22 years, there will be $$ \square $$ students enrolled. (Round to the nearest whole number as needed.) Get more heln

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To predict the number of students enrolled after 22 years with an annual growth rate of $$ 3\% $$, we'll use the exponential growth equation you provided:

$$ y = 17,000 \cdot 1.03^{x} $$

Where:
- $$ y $$ is the number of students after $$ x $$ years.
- $$ 17,000 $$ is the current number of students.
- $$ 1.03 $$ represents a $$ 3\% $$ annual growth rate.

**Step-by-Step Calculation for Part (e):**

1. **Identify the Variables:**
   - Current enrollment ($$ y_0 $$): 17,000 students
   - Growth rate ($$ r $$): 3% or 0.03
   - Number of years ($$ x $$): 22

2. **Plug the Values into the Equation:**
   $$
   y = 17,000 \cdot 1.03^{22}
   $$

3. **Calculate $$ 1.03^{22} $$:**
   - Using a calculator:
   $$
   1.03^{22} \approx 1.917349
   $$

4. **Multiply by the Current Enrollment:**
   $$
   y = 17,000 \times 1.917349 \approx 32,595.933
   $$

5. **Round to the Nearest Whole Number:**
   $$
   y \approx 32,596 \text{ students}
   $$

**Final Answer:**

After 22 years, there will be **32,596** students enrolled.
After 22 years, there will be 32,596 students enrolled.

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