Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![## Educational Content on Population and Loan Calculations
### Population Decline Analysis
**Problem 6:**
Suppose the population of a small town in 1978 was 18,750. In that year, a landfill was built, negatively affecting the population. Each year since, the population decreased by an average of 48 people.
**Tasks:**
- **a)** Derive the linear equation for the town's population, \( P \), \( x \) years after 1978.
**Equation:**
\[
P = 18750 - 48x
\]
- **b)** Interpret the slope from part (a): Each year past 1978, the town's population decreases by 48 people.
### Car Loan Monthly Payments
**Problem 7:**
A car dealership offers financing for a Toyota Prius. The offer results in a monthly payment of $21.60 per $1,000 borrowed over 48 months. Fill out the table to determine the monthly payments for various amounts borrowed.
**Payment Table:**
| Amount Borrowed | Monthly Payment |
|-----------------|-----------------|
| $1,000 | $21.60 |
| $2,000 | $43.20 |
| $3,000 | $64.80 |
| $5,000 | $108.00 |
| $6,000 | $129.60 |
| $9,000 | $194.40 |
| $12,000 | $259.20 |
**Problem 8:**
Based on the table:
- **a)** If your monthly payment is $356.40, the amount borrowed is __________.
- **b)** Monthly payment for borrowing $11,500 is __________.
- **c)** Total repayment for borrowing $11,500 is __________.
**Note:**
- To find the amount borrowed in (a), divide the payment by $21.60 and multiply by $1,000.
- Calculate (b) using the same rate: \( \frac{\$11,500}{\$1,000} \times \$21.60 \).
- For (c), multiply the monthly amount by 48 months.](https://content.bartleby.com/qna-images/question/a0e66dc0-33a7-486a-ab2a-7a4deeb92994/e3603cb9-0b50-4f12-bb03-aaabc73b55f8/ualesn_processed.jpeg)
Transcribed Image Text:## Educational Content on Population and Loan Calculations
### Population Decline Analysis
**Problem 6:**
Suppose the population of a small town in 1978 was 18,750. In that year, a landfill was built, negatively affecting the population. Each year since, the population decreased by an average of 48 people.
**Tasks:**
- **a)** Derive the linear equation for the town's population, \( P \), \( x \) years after 1978.
**Equation:**
\[
P = 18750 - 48x
\]
- **b)** Interpret the slope from part (a): Each year past 1978, the town's population decreases by 48 people.
### Car Loan Monthly Payments
**Problem 7:**
A car dealership offers financing for a Toyota Prius. The offer results in a monthly payment of $21.60 per $1,000 borrowed over 48 months. Fill out the table to determine the monthly payments for various amounts borrowed.
**Payment Table:**
| Amount Borrowed | Monthly Payment |
|-----------------|-----------------|
| $1,000 | $21.60 |
| $2,000 | $43.20 |
| $3,000 | $64.80 |
| $5,000 | $108.00 |
| $6,000 | $129.60 |
| $9,000 | $194.40 |
| $12,000 | $259.20 |
**Problem 8:**
Based on the table:
- **a)** If your monthly payment is $356.40, the amount borrowed is __________.
- **b)** Monthly payment for borrowing $11,500 is __________.
- **c)** Total repayment for borrowing $11,500 is __________.
**Note:**
- To find the amount borrowed in (a), divide the payment by $21.60 and multiply by $1,000.
- Calculate (b) using the same rate: \( \frac{\$11,500}{\$1,000} \times \$21.60 \).
- For (c), multiply the monthly amount by 48 months.
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