Respuesta :
Answer:
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 [tex]t=0,\ S(t)=2[/tex] as the initial thickness is of [tex]2[/tex] meters.
⇒ [tex]S(t) = mt + b[/tex]
⇒ [tex]2=(m\times 0) + b[/tex]
⇒ [tex]2=0+b[/tex]
⇒ [tex]2=b[/tex]
Plugging [tex]t = 3,\ S(t) = 1.25[/tex] as after [tex]3[/tex] weeks it melts gradually.
⇒ [tex]S(t) = mt + b[/tex]
⇒ [tex]1.25=3m + b[/tex]
⇒Putting b=2 from above equation.
⇒ [tex]1.25=3m + 2[/tex]
⇒ [tex]1.25-2=3m + 2-2[/tex]
⇒ [tex]-0.75=3m[/tex]
⇒ [tex]\frac{-0.75}{3} =\frac{3m}{3}[/tex]
⇒ [tex]-0.25=m[/tex]
Plugging the above values in S(t) =mt+b.
⇒ S(t) =mt+b
⇒ [tex]S(t)=-0.25(t)+2[/tex]
Hence
The function's formula is, S(t) = -0.25(t) + 2 i.e. S(t) = 2 - 0.25(t)
