Question

A lake near the Arctic 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 3 weeks, the sheet iS only 1.25 meters thick.
Let y represent the ice sheet's thickness (in meters) after T weeks.

Answer 1

The relationship between the thickness of the ice sheet and the time is given by the slope intercept form which is   y = -0.25x + 2

The general expression for slope intercept is given as:

                y = mx + c          (1)

              Where, m= slope   and c = intercept

According to the question,

Let y be the thickness of the ice

And T be the time in weeks.

At initial week the thickness of the ice = 2 meters

And at 3rd week the thickness of the ice is = 1.25 meters.

Or, we can write as              y(thickness)        T(time in weeks)

                                                      2m                               0

                                                     1.25m                            3

As the thickness is decreasing at a constant rate,

Constant rate is measure as   =  (rate of change in thickness)/(rate of change in time)

                                                     =  (1.25-2)/(3-0)

                                                    =  -0.75/3

                                                     = -0.25

Thus the constant rate at which the thickness is decreasing is -0.25 which is also known as the slope of a line.

That is ,  m= -0.25

For the slope intercept the value of c is given by putting the value of y = 2m  and x= 0weeks  in equation (1) we get

  Thus,       2 = m*0 + c

                   c = 2

Putting the required value in equation (1)

          y = -0.25x + 2

Which is the required relationship between the thickness and the time.

Learn more about slope intercept form here : https://brainly.com/question/19440459

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