The number of students enrolled at a college is 17,000 and grows each year. Complete parts (a) through
(e).
c) To find the number of students enrolled after one year, you calculate .
d) Complete the equation to find the number of students enrolled after years.
e) Use your equation to predict the number of students enrolled after 22 years.
Ater 22 years, there will be students enrolled.
(Round to the nearest whole number as needed.)
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Ask by Campbell Norris. in the United States

Jan 24,2025

Question

The number of students enrolled at a college is 17,000 and grows each year. Complete parts (a) through
(e).
c) To find the number of students enrolled after one year, you calculate .
d) Complete the equation to find the number of students enrolled after years.
e) Use your equation to predict the number of students enrolled after 22 years.
Ater 22 years, there will be students enrolled.
(Round to the nearest whole number as needed.)
Get more heln

Ask by Campbell Norris. in the United States

Jan 24,2025

UpStudy AI · Accepted Answer

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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