Question

A lake near the artic circle is covered by a 2 meter thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate. After three weeks, the sheet is only 1.25 meters thick. let y represent the ice sheet’s thickness (in meters) after x weeks.

Answer 1

`\displaystyle y=2-0.25x`

Explanation:

Linear Relationship

When two variables follow a linear relationship, the function has a constant rate of decrease or increase. We can completely define a line by knowing 2 points P(a,b) and Q(c,d) by using the two-point formula

`\displaystyle y-b=(d-b)/(c-a)(x-a)`

The thickness of the sheet of ice is a function of time x in weeks. We know when x is zero (during the cold winter months), the thickness is 2 meters. 3 weeks, the sheet is 1.25 meters thick. This gives us two points to work with P(0,2) Q(3,1.25). Replacing values in the formula

`\displaystyle y-2=(1.25-2)/(3)x`

Operating

`\displaystyle y-2=-0.25x`

Rearranging

`\displaystyle y=2-0.25x`