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At the beginning of year 1, the population of the country of Freedonia has 3450 people. Each year, the population grows in two ways. One is through birth rates: each year, the number of newborns is 5% of the population at the beginning of the year. The second way the population grows in through immigration: the country allows exactly 25 people into the country each year (and that's how many actually enter the country each year). No one dies in Freedonia, and no one leaves. Write and solve a recurrence equation (with an initial condition) that represents the population of Freedonia at the beginning of year n. (For the purposes of this problem, we allow “fractional" people.)

At the beginning of year 1, the population of the country of Freedonia has 3450 people. Each year, the population grows in two ways. One is through birth rates: each year, the number of newborns is 5% of the population at the beginning of the year. The second way the population grows in through immigration: the country allows exactly 25 people into the country each year (and that's how many actually enter the country each year). No one dies in Freedonia, and no one leaves. Write and solve a recurrence equation (with an initial condition) that represents the population of Freedonia at the beginning of year n. (For the purposes of this problem, we allow “fractional" people.)

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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At the beginning of **year 1**, the population of the country of Freedonia has 3450 people. Each year, the population grows in two ways. One is through birth rates: each year, the number of newborns is 5% of the population at the beginning of the year. The second way the population grows is through immigration: the country allows exactly 25 people into the country each year (and that’s how many actually enter the country each year). No one dies in Freedonia, and no one leaves. Write and solve a recurrence equation (with an initial condition) that represents the population of Freedonia at the beginning of year **n**. (For the purposes of this problem, we allow “fractional” people.) Solve the recurrence equation step by step.
Transcribed Image Text:At the beginning of **year 1**, the population of the country of Freedonia has 3450 people. Each year, the population grows in two ways. One is through birth rates: each year, the number of newborns is 5% of the population at the beginning of the year. The second way the population grows is through immigration: the country allows exactly 25 people into the country each year (and that’s how many actually enter the country each year). No one dies in Freedonia, and no one leaves. Write and solve a recurrence equation (with an initial condition) that represents the population of Freedonia at the beginning of year **n**. (For the purposes of this problem, we allow “fractional” people.) Solve the recurrence equation step by step.
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