A certain population declines by 7% each year. What is the percentage decline each month? (Round your answer to two decimal places.) 19

Algebra and Trigonometry (6th Edition)
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Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Educational Text:**

**Population Decline Problem**

A certain population declines by 7% each year. What is the percentage decline each month? *(Round your answer to two decimal places.)* 

---

To solve this problem, you need to calculate the monthly percentage decline from the annual decline percentage. You can use the formula for compound interest decay:

\[ 
(1 - \text{annual decline rate})^{\frac{1}{12}} = 1 - \text{monthly decline rate}
\]

Given:
- Annual decline rate = 7% or 0.07

Calculation:
1. Compute \( (1 - 0.07)^{\frac{1}{12}} \)
2. Subtract the result from 1 to get the monthly decline rate.
3. Multiply by 100 to convert it to a percentage.
4. Round the final answer to two decimal places.

This approach ensures an accurate breakdown of the yearly decline into monthly increments.
Transcribed Image Text:**Educational Text:** **Population Decline Problem** A certain population declines by 7% each year. What is the percentage decline each month? *(Round your answer to two decimal places.)* --- To solve this problem, you need to calculate the monthly percentage decline from the annual decline percentage. You can use the formula for compound interest decay: \[ (1 - \text{annual decline rate})^{\frac{1}{12}} = 1 - \text{monthly decline rate} \] Given: - Annual decline rate = 7% or 0.07 Calculation: 1. Compute \( (1 - 0.07)^{\frac{1}{12}} \) 2. Subtract the result from 1 to get the monthly decline rate. 3. Multiply by 100 to convert it to a percentage. 4. Round the final answer to two decimal places. This approach ensures an accurate breakdown of the yearly decline into monthly increments.
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