Question

A lake near the Arctic Circle is covered by a 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 rate of 0.2 meters per week. After 7 weeks, the sheet is only 2.42 meters thick.
Let S(t), denote the ice sheet's thickness S (measured in meters) as a function of time t (measured in weeks).

Write the function's formula.

S(t)=________

Answer 1

We know that the thickness of the lake decreases at a rate of 0.2 meters per week, so we can write:
S(t)=-0.2t+4
we also know that after 7 weeks, the sheet is only 2.42 meters thick, which means we can write:
S(7)=2.42
S(7)=-0.2*7+X
S(7)=-1.4+X
2.42=-1.4+X
X=3.82
So, the function is: S(t)=--0.2*t+3.82

Answer 2

Answer:

S(t) = 3.82 - 0.2t

Step-by-step explanation:

After 7 weeks, the ice is 2.42 meters thick.  The ice loses 0.2 meters of thickness per week; this means on the 7th week, it has lost 7(0.2) = 1.4 meters of thickness.

This means the ice started at 2.42+1.4 = 3.82 meters thick.

Our function will start at the original thickness of the ice, 3.82 meters.

Since the ice is losing thickness, we will subtract; it loses at a rate of 0.2 meters per week (t), which gives us 0.2t.  This is subtracted from the original, 3.82 meters, giving us

S(t) = 3.82 - 0.2t