Question

A scientist cools some water at a constant rate. The graph and table show
how the temperature of the water changes with time.
Which function models this situation?
Water Temperature.
55
50
45
40
35
30
25
20
15
10
4
5 6
7
8
Time (minutes)
Temperature (°C)
..
5
9 10

Answer 1

A function assigns the values. The function for this model can be written as y=-4x+50.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

As it can be seen from the graph that the function is linear, therefore, we can write,

y = mx + c

Given two points of the graph, therefore, we can write for the first point,

30 = m(5) + c

30 = 5m + c

c = 30 - 5m

Also, for the second point,

y = mx + c

26 = 6m + c

Substitute the value of c,

26 - 6m = 30 - 5m

-6m + 5m = 30 - 26

-m = 4

m = -4

Now, substitute the value of m in any one of the equation formed above,

c = 30 - 5m

c = 30 - 5(-4)

c = 50

Hence, the function for this model can be written as y=-4x+50.

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