Question

A lake near the Arctic Circle is covered by a

22

2

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

33

3

3

weeks, the sheet is only

1.251.25

1.25

1, point, 25

meters thick.

Let

SS

S

S

represent the ice sheet's thickness (in meters) after

tt

t

t

weeks.

Answer 1

Answer:

S = 2 - 0.25W

Step-by-step explanation:

A lake near the Arctic Circle is covered by a  2 meters thick sheet of ice during the cold winter months.

At the warm air of spring gradually melts the ice thickness gradually.

Therefore, the equation that models the situation is S = 2 - bW ....... (1), where S is the remaining thickness of the ice sheet and W is the number of weeks passed and b is the rate of decrease of ice sheet thickness with respect to the number of weeks.

Now, putting W = 3 weeks and S = 1.25 meters in the equation (1) we get,

1.25 = 2 - 3b

⇒ 3b = 0.75

⇒ b = 0.25 meters per week.

Therefore, the equation (1) becomes S = 2 - 0.25W (Answer)