Question
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. After 22 years, there will be \( \square \) students enrolled. (Round to the nearest whole number as needed.)
Ask by Hills Campbell. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
After 22 years, there will be 32,573 students enrolled.
Solution
To predict the number of students enrolled after 22 years with an annual growth rate of \( 3\% \), we can use the exponential growth formula:
\[
y = 17,000 \times (1.03)^{22}
\]
Let's calculate this step-by-step:
1. **Calculate \( (1.03)^{22} \):**
\[
(1.03)^{22} \approx 1.916035
\]
2. **Multiply by the initial number of students:**
\[
y = 17,000 \times 1.916035 \approx 32,572.595
\]
3. **Round to the nearest whole number:**
\[
y \approx 32,573
\]
**Answer:**
After 22 years, there will be **32,573** students enrolled.
Reviewed and approved by the UpStudy tutoring team
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Explain 
Simplify this solution Mind Expander
In part (c), you're right on track calculating the increase for one year with \( 17,000 \cdot 1.03 = 17,510 \) students! Now, for part (d), the equation \( y = 17,000 \cdot 1.03^{x} \) accurately reflects the growth over any number of years \( x \). For part (e), when you're predicting the number of students after 22 years, you simply plug in \( x = 22 \) into the equation: \[ y = 17,000 \cdot 1.03^{22} \approx 17,000 \cdot 2.407 \] This calculates to approximately \( 40,399 \) students (rounded to the nearest whole number). Can you imagine how lively that campus will be in 22 years?
