The linear trend of sales of a company is 650000 in 1995 and it rises ...
**Trend Equation**
The trend equation represents the linear relationship between the year and the sales of a company. It can be used to predict future sales based on the historical data. In this case, the given information states that the sales of the company in 1995 were 650,000 and it rose by 16,500 per year.
Let's assume that 'x' represents the number of years since 1995 and 'y' represents the sales of the company in that year.
The trend equation is given by:
y = mx + c
Where:
- 'm' is the slope or the rate of change of sales per year
- 'c' is the y-intercept or the sales in the base year (1995)
**Calculating the Slope (m)**
The given information states that the sales of the company rise by 16,500 per year. Therefore, the slope (m) can be calculated as follows:
m = change in y / change in x
= 16,500 / 1
= 16,500
Therefore, the slope (m) is 16,500.
**Calculating the Y-Intercept (c)**
The given information states that the sales of the company in 1995 were 650,000. Therefore, the y-intercept (c) can be calculated as follows:
c = y - mx
= 650,000 - (16,500 * 0)
= 650,000
Therefore, the y-intercept (c) is 650,000.
**Final Trend Equation**
Now that we have calculated the slope (m) and the y-intercept (c), we can write the trend equation as follows:
y = 16,500x + 650,000
This equation represents the linear trend of the sales of the company. It allows us to predict the sales in any given year based on the number of years since 1995.
**Analysis of the Company**
Based on the trend equation, the sales of the company have been steadily increasing by 16,500 per year since 1995. This indicates a positive growth trend for the company.
By using the trend equation, we can also predict the sales of the company in future years. For example, if we want to calculate the sales in 2022 (27 years since 1995), we can substitute x = 27 into the equation:
y = 16,500 * 27 + 650,000
= 1,759,500 + 650,000
= 2,409,500
Therefore, based on the trend equation, the predicted sales of the company in 2022 would be 2,409,500.
It is important to note that the trend equation assumes a linear relationship between the year and the sales. It may not capture all the factors that can influence the sales of the company, such as market conditions, competition, economic factors, etc. Therefore, it should be used as a guide and not as an absolute predictor of future sales.