Question

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 1

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.

`S_n=(a_1(1-r^n))/(1-r)`

Using the given information, we have

`S_(10)=(5000(1-(1.05)^(10)))/(1-1.05)=(5000\cdot(-0.63))/(-0.05)\approx63,000`

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