Question
A new factory In a small town has an annual payroll of 6 million. It is expected 50% of this money will be spent in the town by factory personnel. The people in the town who receive this money are expected to spend 50% of what they receive in the town , and so on. What is the total of all of this spending , called the total economic impact on the town each year?
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Answer to a math question A new factory In a small town has an annual payroll of 6 million. It is expected 50% of this money will be spent in the town by factory personnel. The people in the town who receive this money are expected to spend 50% of what they receive in the town , and so on. What is the total of all of this spending , called the total economic impact on the town each year?
Hermann
4.6120 Answers
1. Identify the initial spending and the common ratio:
- Initial Spending: 6,000,000
- Common Ratio, r = 0.5
2. Substitute into the formula for the sum of an infinite geometric series:
S = \frac{\text{Initial Spending}}{1 - r}
3. Calculate:
S = \frac{6,000,000}{1 - 0.5}
4. This results in:
S = \frac{6,000,000}{0.5}
5. Simplify the division:
S = 12,000,000
6. Therefore, the total economic impact is 12,000,000
- Initial Spending:
- Common Ratio,
2. Substitute into the formula for the sum of an infinite geometric series:
3. Calculate:
4. This results in:
5. Simplify the division:
6. Therefore, the total economic impact is
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