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An island is colonized by immigration from the mainland, where there are 500 species. Let the number of species on the island at time t (in years) equal y, where y = f(t). Suppose the rate at which new species immigrate to the island is = 0.02 500 - y dt Use Euler's method with h = 0.5 years to approximate y when t= 5 years if there were 10 species initially. There will be approximately species when t= 5 years. (Round the final answer to the nearest whole number as needed. Round all intermediate values to six decimal places as needed.)

An island is colonized by immigration from the mainland, where there are 500 species. Let the number of species on the island at time t (in years) equal y, where y = f(t). Suppose the rate at which new species immigrate to the island is = 0.02 500 - y dt Use Euler's method with h = 0.5 years to approximate y when t= 5 years if there were 10 species initially. There will be approximately species when t= 5 years. (Round the final answer to the nearest whole number as needed. Round all intermediate values to six decimal places as needed.)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 13EQ
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An island is colonized by immigration from the mainland, where there are 500 species. Let the number of species on the island at time t (in years) equal y, where y = f(t). Suppose the rate at which new species dy = 0.02 500 - dt immigrate to the island is Use Euler's method with h = 0.5 years to approximate y when t= 5 years if there were 10 species initially. There will be approximately species when t= 5 years. (Round the final answer to the nearest whole number as needed. Round all intermediate values to six decimal places as needed.)
Transcribed Image Text:An island is colonized by immigration from the mainland, where there are 500 species. Let the number of species on the island at time t (in years) equal y, where y = f(t). Suppose the rate at which new species dy = 0.02 500 - dt immigrate to the island is Use Euler's method with h = 0.5 years to approximate y when t= 5 years if there were 10 species initially. There will be approximately species when t= 5 years. (Round the final answer to the nearest whole number as needed. Round all intermediate values to six decimal places as needed.)
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