Question

A manufacturer producing a new product, estimates the annual sales to be 9,600 units. Each year, 8% of the units that have been sold will become inoperative. So, 9,600 units will be in use after 1 year, [9,600 0.92(9,600)] units will be in use after 2 years, and so on. How many units will be in use after n years

Answer 1

After n years, 120,000(1 - 0.92ⁿ) units, will be in use.

Explanation:

Given;

estimated annual sales, a = 9600 units

determine common ratio, r;

`r = 1 - (8)/(100)\\\\r = 0.92`

sum of the units in use after n years is calculated by applying sum of nth term;

`S_n = (a)/(1-r) (1-r^n)`

`S_n = (9600)/(1-0.92) (1-0.92^n)\\\\S_n = (9600)/(0.08) (1-0.92^n)\\\\S_n = 120,000(1-0.92^n) \ units`

Therefore, after n years, 120,000(1 - 0.92ⁿ) units, will be in use.