Sequence and Series - Problems involving inequalities

Portable telephones are first sold in the country Cellmania in \(1990\). During \(1990\), the number of units sold is \(160\). In \(1991\), the number of units sold is \(240\) and in \(1992\), the number of units sold is \(360\)

In \(1993\) it was noticed that the annual sales formed a geometric sequence with first term \(160\), the \(2^{\mathrm{nd}}\) and \(3^{\mathrm{rd}}\) terms being \(240\) and \(360\) respectively.

1. What is the common ratio of this sequence?[1]

Assume that this trend in sales continues.

2. How many units will be sold during \(2002\)?[3]
3. In what year does the number of units sold first exceed \(5000\)?[4]

Between \(1990\) and \(1992\), the total number of units sold is \(760\).

4. What is the total number of units sold between \(1990\) and \(2002\)?[2]

During this period, the total population of Cellmania remains approximately \(80 \ 000\).

5. Use this information to suggest a reason why the geometric growth in sales would not continue.[1]