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 x weeks.

Answer 1

Y=--0.2x+3.82

Explanation:

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

The answer would be y-intercept and a point that is NOT an intercept

Explanation:

To describe a point on the graph, we need a corresponding

(x,y)(x,y)

(x,y)

left parenthesis, x, comma, y, right parenthesis

pair.

In our case, these are corresponding values of weeks since spring arrives and thickness of ice.

weeks since spring arrivedthickness of ice↓↓(x,y)\begin{aligned} \scriptsize\text{weeks since spring arrived}&\quad\scriptsize\text{thickness of ice} \\ \downarrow&\quad\downarrow \\ \large (x &,\quad\large y) \end{aligned}

weeks since spring arrived

↓

(x

​

thickness of ice

↓

,y)

​

To describe the slope of the graph, we need information about the rate of change of the relationship.

In our case, this is the rate at which the thickness of ice changes over time (in meters per week).

Hint #2

2 / 4

The ice is

22

2

2

meters thick at the start of spring, when

00

0

0

weeks have passed. This corresponds to the point

(0,2)(0,2)

(0,2)

left parenthesis, 0, comma, 2, right parenthesis

and is a

yy

y

y

-intercept.

Hint #3

3 / 4

After

33

3

3

weeks, the sheet is only

1.251.25

1.25

1, point, 25

meters thick. This corresponds to the point

(3,1.25)(3,1.25)

(3,1.25)

left parenthesis, 3, comma, 1, point, 25, right parenthesis

and is not an intercept.

Hint #4

4 / 4

The

yy

y

y

-intercept and a point that is not an intercept is given