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

Answer:

$\displaystyle y=2-0.25x$

Step-by-step 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

$\displaystyle y-b=\frac{d-b}{c-a}(x-a)$

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

$\displaystyle y-2=\frac{1.25-2}{3}x$

Operating

$\displaystyle y-2=-0.25x$

Rearranging

$\displaystyle y=2-0.25x$