The Birch Company, a manufacturer of electrical circuit boards, has manufactured the following number of units over the past 5 years:
1992 12,500
1993 13,250
1994 14,310
1995 15,751
1996 17,630
Calculate the average percentage increase in units produced over this time period, and use this to estimate production for 1999
To calculate the average percentage increase in units produced over the 5-year period, follow these steps:
Step 1: Determine the percentage increase in units produced for each consecutive year.
- Percentage increase = ((new value - old value) / old value) * 100
For the given data:
- In 1993: Percentage increase = ((13,250 - 12,500) / 12,500) * 100 = 6%
- In 1994: Percentage increase = ((14,310 - 13,250) / 13,250) * 100 = 7.99%
- In 1995: Percentage increase = ((15,751 - 14,310) / 14,310) * 100 = 10.08%
- In 1996: Percentage increase = ((17,630 - 15,751) / 15,751) * 100 = 11.91%
Step 2: Calculate the average percentage increase by summing up the percentage increases from Step 1 and dividing by the number of years.
- Average percentage increase = (6 + 7.99 + 10.08 + 11.91) / 4 = 8.745%
Step 3: Estimate production for 1999 by applying the average percentage increase to the units produced in 1996.
- Production in 1999 = (17,630) * (1 + (8.745 / 100))
Hence, the estimated production for 1999 is approximately 19,166 units.
To calculate the average percentage increase in units produced over the 5-year period, you can follow these steps:
1. Calculate the percentage increase in units produced each year by using the formula:
Percentage Increase = ((New Value - Old Value) / Old Value) * 100
For example, for the first year (1992 to 1993), the percentage increase is:
((13,250 - 12,500) / 12,500) * 100 = 6%
2. Repeat this calculation for each year in the data set, resulting in a list of percentage increases.
3. Calculate the average percentage increase by summing up all the percentage increases and dividing by the number of years.
Once you have the average percentage increase, you can use it to estimate the production for 1999 by following these steps:
1. Start with the last known production value (17,630 in 1996).
2. Calculate the estimated increase in production for each subsequent year by multiplying the last known production value by the average percentage increase.
For example, for 1997:
Estimated Production = 17,630 * Average Percentage Increase
3. Add the estimated increase in production to the last known production value to get the estimated production for the subsequent year.
4. Repeat this calculation for each subsequent year until you reach the target year (1999).
Keep in mind that this estimation assumes a consistent growth rate based on the average percentage increase calculated for the previous 5 years and may not be accurate if there are significant changes in the factors influencing production.
Let me know if you need further assistance with the calculations.