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6. Suppose the population of a small town in 1978 was 18,750. In that year, a landfill was built and has had a negative effect on the population of the town, such that for each year past 1978, the population has decreased, on average by 48 people. a) Find the linear equation that describes the town's population, P for x years after 1978. P= b) The correct interpretation of slope in the linear equation from part a is: For each year by. past 1978, the town's population people.

6. Suppose the population of a small town in 1978 was 18,750. In that year, a landfill was built and has had a negative effect on the population of the town, such that for each year past 1978, the population has decreased, on average by 48 people. a) Find the linear equation that describes the town's population, P for x years after 1978. P= b) The correct interpretation of slope in the linear equation from part a is: For each year by. past 1978, the town's population people.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
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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