Question

A computer company uses the linear model y = -21x + 13,082 to predict the decline in sales of a computer after it has been on the market more than one year. If x is the number of months after the first year and y is the number of computers sold during that month, how many computers will be sold 11 months after the first year?

Answer 1

The number of computers sold each month after the first year is a decreasing arithmetic progression.

The first term of the progression (sales in first month after the first year) is:

$$m_{1}=13082-21*1=13061$$

The general view of the progression term is:

$$m_{n}=13061-21*(n-1)$$

The sum of sales for n is:

$$S_{n}=\frac {2*m_{1}-(n-1)*21} {2}*n$$

The sum of sales for 11 monthes is:

$$S_{11}=\frac {2*13061-(11-1)*21} {2}*11=142516$$

Answer: 142516 computers.