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A car company has an estimate of selling 5000 cars in 2010 and for the next 10 years to increase sales by 5% per year compared to the previous year. It determines how many cars the company intends to sell in that period.

Answer :

We know that

• The initial value is 5000 cars.

,

• The rate of sales per year is 5%. (r = 1.05%)

,

• The total period of time is 10 years.

We have to use the formula for the sum of geometric sequences.

[tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex]

Using the given information, we have

[tex]S_{10}=\frac{5000(1-(1.05)^{10})}{1-1.05}=\frac{5000\cdot(-0.63)}{-0.05}\approx63,000[/tex]

Hence, the number of cars intended to be sold in 10 years is 63,000.

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