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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

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onyebuchinnaji

Answer:

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

Step-by-step explanation:

Given;

estimated annual sales, a = 9600 units

determine common ratio, r;

[tex]r = 1 - \frac{8}{100}\\\\r = 0.92[/tex]

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

[tex]S_n = \frac{a}{1-r} (1-r^n)[/tex]

[tex]S_n = \frac{9600}{1-0.92} (1-0.92^n)\\\\S_n = \frac{9600}{0.08} (1-0.92^n)\\\\S_n = 120,000(1-0.92^n) \ units[/tex]

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

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