Video Transcript
Once workers start to construct a building, the height of the building increases at a linear rate. After seven weeks, the height of the building is 21 metres. Which of the following functions best models the relationship between the height ℎ of 𝑤 in metres of the building and the number of weeks 𝑤 from when they start construction? Is it option A) ℎ of 𝑤 is equal to 21 𝑤, B) ℎ of 𝑤 is equal to seven 𝑤, C) ℎ of 𝑤 is equal to 21 plus 𝑤, or D) ℎ of 𝑤 is equal to three 𝑤.
As the height of the building increases at a linear rate, we know that each week, it will increase by the same height. After seven weeks, we were told that the height of the building is equal to 21 metres. We need to calculate how many metres the building is increased by each week. Dividing seven by seven gives us one. This will enable us to calculate the height of the building after one week.
As we have divided the number of weeks by seven, we need to divide the height by seven. 21 metres divided by seven is equal to three metres. Therefore, after one week, the height of the building was three metres. Once again, as we were told that the building increases at a linear rate, the height of the building will increase by three metres each week.
In order to calculate the height of the building at any time, we need to multiply the number of weeks by three metres. This means that ℎ of 𝑤 is equal to three 𝑤. For example, after seven weeks, the height of the building will be three multiplied by seven. Three multiplied by seven is equal to 21.
The correct answer from our four options was option D: ℎ of 𝑤 is equal to three 𝑤.
