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4. The population of shrimp in the Gulf of Mexico has been declining due to environmental declines in the region. There are around 3.4 million tons caught per year. However, that has been decreasing at a rate of 0.02% a year. What will be the estimated population in 75 years? Find the explicit formula. a. What are the first 3 terms? b. Еxplicit: a, = %3! f(n) = c. What will be the estimated population in 75 years? f( )=

4. The population of shrimp in the Gulf of Mexico has been declining due to environmental declines in the region. There are around 3.4 million tons caught per year. However, that has been decreasing at a rate of 0.02% a year. What will be the estimated population in 75 years? Find the explicit formula. a. What are the first 3 terms? b. Еxplicit: a, = %3! f(n) = c. What will be the estimated population in 75 years? f( )=

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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**Problem 4: Declining Shrimp Population in the Gulf of Mexico** **Context:** The population of shrimp in the Gulf of Mexico has been declining due to environmental changes in the area. Currently, approximately 3.4 million tons are harvested annually. Unfortunately, this number decreases by 0.02% per annum. The task is to estimate the shrimp population 75 years into the future and develop an explicit formula for this estimation. **Tasks:** a. **Identify the First 3 Terms:** b. **Explicit Formula Development:** - Initial amount \( a_1 = \) - Rate of decline \( r = \) - Function \( f(n) = \) c. **Future Estimation:** - Estimated population in 75 years \( f( \, ) = \) **Directions:** You're encouraged to calculate and fill in the necessary values such as the initial amount, rate of decline, function formula, and future population estimation. This exercise involves understanding exponential decay and applying it to real-world contexts.
Transcribed Image Text:**Problem 4: Declining Shrimp Population in the Gulf of Mexico** **Context:** The population of shrimp in the Gulf of Mexico has been declining due to environmental changes in the area. Currently, approximately 3.4 million tons are harvested annually. Unfortunately, this number decreases by 0.02% per annum. The task is to estimate the shrimp population 75 years into the future and develop an explicit formula for this estimation. **Tasks:** a. **Identify the First 3 Terms:** b. **Explicit Formula Development:** - Initial amount \( a_1 = \) - Rate of decline \( r = \) - Function \( f(n) = \) c. **Future Estimation:** - Estimated population in 75 years \( f( \, ) = \) **Directions:** You're encouraged to calculate and fill in the necessary values such as the initial amount, rate of decline, function formula, and future population estimation. This exercise involves understanding exponential decay and applying it to real-world contexts.
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