Consider a bank with a strange rule for giving out interest. After the first year (and every other odd-numbered year) you hold the account, your money increases by 100 percent. After every even-numbered year (not including year 0), your money decreases by 60 percent. Let ao be the amount of money you initially put in the account. (i) Define a recursive sequence for the amount of money you would have after n years. (ii) Write a sequence for the amount of money you would have in your account after m number of EVEN years have elapsed. Your sequence should only depend on the initial amount of money in your account, ao, and m. (iii) Does the amount of money in your account converge or diverge as m → ∞. If it converges, to what value?
Consider a bank with a strange rule for giving out interest. After the first year (and every other odd-numbered year) you hold the account, your money increases by 100 percent. After every even-numbered year (not including year 0), your money decreases by 60 percent. Let ao be the amount of money you initially put in the account. (i) Define a recursive sequence for the amount of money you would have after n years. (ii) Write a sequence for the amount of money you would have in your account after m number of EVEN years have elapsed. Your sequence should only depend on the initial amount of money in your account, ao, and m. (iii) Does the amount of money in your account converge or diverge as m → ∞. If it converges, to what value?
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:Consider a bank with a strange rule for giving out interest. After the first year
(and every other odd-numbered year) you hold the account, your money increases by 100 percent.
After every even-numbered year (not including year 0), your money decreases by 60 percent. Let
ao be the amount of money you initially put in the account.
(i) Define a recursive sequence for the amount of money you would have after n years.
(ii) Write a sequence for the amount of money you would have in your account after
m number of EVEN years have elapsed. Your sequence should only depend on the initial
amount of money in your account, ao, and m.
(iii) Does the amount of money in your account converge or diverge as m → ∞. If it
converges, to what value?
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