A scientist noticed that the population of a certain country could be represented by the following recursive relation ak = ak-1 + 2·3* for each integer k > 2 a1 = 2 (where a, represents the population in millions at the beginning of 2001, az is the population in millions at the beginning of 2002, and so on). A different researcher found that the population of the same country could be represented. by the following explicit formula an = 3n+1 – 7 for all integers n >1 (where a, represents the population in millions at the beginning of 2001, az is the population in millions at the beginning of 2002, and so on). Prove that both scientists are correct by proving the formulas are equivalent.
A scientist noticed that the population of a certain country could be represented by the following recursive relation ak = ak-1 + 2·3* for each integer k > 2 a1 = 2 (where a, represents the population in millions at the beginning of 2001, az is the population in millions at the beginning of 2002, and so on). A different researcher found that the population of the same country could be represented. by the following explicit formula an = 3n+1 – 7 for all integers n >1 (where a, represents the population in millions at the beginning of 2001, az is the population in millions at the beginning of 2002, and so on). Prove that both scientists are correct by proving the formulas are equivalent.
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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Transcribed Image Text:5. A scientist noticed that the population of a certain country could be represented by the
following recursive relation
ak = ak-1 + 2· 3* for each integer k >2
a1
2
(where a, represents the population in millions at the beginning of 2001, az is the
population in millions at the beginning of 2002, and so on).
A different researcher found that the population of the same country could be represented
by the following explicit formula
3n+1 – 7 for all integers n > 1
an
(where a, represents the population in millions at the beginning of 2001, az is the
population in millions at the beginning of 2002, and so on).
Prove that both scientists are correct by proving the formulas are equivalent.
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