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3. The United States population grows at a rate of 0.5% a year. We have around 328.2 million. What will the population be in 50 years? Write the recursive and explicit formula. a. What are the first 3 terms? b. Recursive: a = а, с. Еxplicit: a = f(n) =

3. The United States population grows at a rate of 0.5% a year. We have around 328.2 million. What will the population be in 50 years? Write the recursive and explicit formula. a. What are the first 3 terms? b. Recursive: a = а, с. Еxplicit: a = f(n) =

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 3: Population Growth Calculation** The United States population grows at a rate of 0.5% per year. Currently, the population is approximately 328.2 million. What will the population be in 50 years? You are required to write both the recursive and explicit formulae for this scenario. **a. What are the first 3 terms?** **b. Recursive Formula:** - Initial term (\(a_1\)): - Recursive formula (\(a_n\)): **c. Explicit Formula:** - Initial term (\(a_1\)): - Growth rate (\(r\)): - Explicit function (\(f(n)\)): **d. Population in 50 Years:** Determine the population in 50 years by finding the 51st term (since the calculation for the 50th year requires the 51st term): - \(f(\_\_\_) =\) This problem involves calculating future population using compound growth formulas. Use the given data to derive the correct recursive and explicit expressions, then find the population for the given time frame.
Transcribed Image Text:**Problem 3: Population Growth Calculation** The United States population grows at a rate of 0.5% per year. Currently, the population is approximately 328.2 million. What will the population be in 50 years? You are required to write both the recursive and explicit formulae for this scenario. **a. What are the first 3 terms?** **b. Recursive Formula:** - Initial term (\(a_1\)): - Recursive formula (\(a_n\)): **c. Explicit Formula:** - Initial term (\(a_1\)): - Growth rate (\(r\)): - Explicit function (\(f(n)\)): **d. Population in 50 Years:** Determine the population in 50 years by finding the 51st term (since the calculation for the 50th year requires the 51st term): - \(f(\_\_\_) =\) This problem involves calculating future population using compound growth formulas. Use the given data to derive the correct recursive and explicit expressions, then find the population for the given time frame.
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