When the construction company established the construction site at the beginning of 2023, it employed 390 staff to work on the site.
The staff comprised 330 construction workers
At the beginning of each year, staff can choose to stay in the same job, move to a different job on the site, or leave the site
The transition diagram below shows the proportion of staff who are expected to change their job at the site each year.
This situation can be modelled by the recurrence relation
- Calculate the predicted percentage decrease in the number of foremen
on the site from 2023 to 2025. (1 mark)
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- Determine the total number of staff on the site in the long term. (1 mark)
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To encourage more construction workers
Matrix
The site always requires at least 330 construction workers.
To ensure that this happens, the company hires an additional 190 construction workers
The matrix
- How many more staff are there on the site in 2024 than there were in 2023 ? (1 mark)
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- Based on this new model, the company has realised that in the long term there will be more than 200 foremen on site.
- In which year will the number of foremen first be above 200? (1 mark)
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