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

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 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.

The function's formula is, S(t) = -0.25(t) + 2

Step-by-step explanation:

Given:

That there is gradual decrease in the thickness of the ice of Arctic circle.

S(t) denote the ice sheet's thickness S ( measured in meters) as a function of time (measured in weeks).

Initial thickness of the sheet of ice, S(t) = 2 m

Numbers of weeks required to melt = 3

After melting its final thickness is = 1.25 m

Considering the decrease at a constant rate we can say that it follows linear pattern or linear equation.

So,

The equation will be of the form y = m(x) + b

Re-arranging the terms:

We have:

S(t) = mt + b

Now we have to find the slope (m) and y-intercept value (b).

Plugging as the initial thickness is of meters.

⇒

⇒

⇒

⇒

Plugging as after weeks it melts gradually.

⇒

⇒

⇒Putting b=2 from above equation.

⇒

⇒

⇒

⇒

⇒

Plugging the above values in S(t) =mt+b.

⇒  S(t) =mt+b

⇒

Hence

The function's formula is, S(t) = -0.25(t) + 2 i.e. S(t) = 2 - 0.25(t)

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.