In-order-to-monitor-buses-in-a-travel-agency-the-manager-decides-to-monitor-the-number-of-break-downs-of-the-buses-using-the-sequence-x-n-defined-by-x-n-1-1-05-x-n-4-Given-that-x-0-40-

Question Number 159122 by physicstutes last updated on 13/Nov/21

In order to monitor buses in a travel

agency, the manager decides to monitor

the number of break downs of the buses

using the sequence {x_{n}} defined by

x_{n + 1} = 1.05 x_{n} + 4 . Given that x_{0} = 40 .

is the number of break downs by the buses

from the 1^{st} of january 2000, and that

for every n \in N, we denote x_{n} the number

of breakdowns of the buses as from 1^{st}

of january of the year (2000 + n)

(a) Calculate x_{1}, x_{2}, x_{3}

(b) Consider the sequence {y_{n}} defined

by y_{n} = x_{n} + 80 for all n \in N

(i) express y_{n + 1} in terms of y_{n} and

deduce the nature of the sequence {y_{n}} .

(ii) Express y_{n} in terms of n . deduce x_{n}

in terms of n

(iv) find the number of break downs

that will be registered by 1^{st} january

2021 .