Question

A lake near the Arctic Circle is covered by a 222-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 3 weeks, the sheet is only 1.25 meters thick Let y represent the ice sheet's thickness (in meters) after x weeks. Complete the equation for the relationship between the thickness and number of weeks. y=

Answer 1

Given:

Initial ice sheet's thickness = 2 meter

After 3 weeks, the ice sheet's thickness = 1.25 meters

To find:

The equation for the relationship between the thickness and number of weeks.

Solution:

Let y represent the ice sheet's thickness (in meters) after x weeks.

Initial ice sheet's thickness = 2 meter

It means, the equation of relation must be satisfy by the point (0,2).

After 3 weeks, the ice sheet's thickness = 1.25 meters

It means, the equation of relation must be satisfy by the point (3,1.25).

If a linear function passes through two points, then the equation is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

`y-2=(1.25-2)/(3-0)(x-0)`

`y-2=(-0.75)/(3)x`

`y-2=-0.25x`

Add 2 on both sides.

`y=-0.25x+2`

Therefore, the required equation for the given relation is
`y=-0.25x+2`.