Question

a) Find the rate of change between the two endpoints (x = 200 to x = 2200) 35 (200,25) Temperature (0) 25 20 15 10 5 b) Explain what the above rate of change means to someone who doesn't understand rate of change. (2200, 13) 0 2000 Altitude (m) c) Find the range of the graph.

Answer 1

Answers:

a) Rate of change = -0.006

b) The rate of change shows that every time we add 1 meter to the altitude, the temperature will decrease 0.006 °C

c) Range = [13, 25]

Step-by-step explanation:

The rate change between two points can be calculated as:

`\text{rate}=(y_2-y_1)/(x_2-x_1)`

Where (x1, y1) and (x2, y2) are the endpoints. So replacing (x1, y1) by (200, 25) and (x2, y2) by (2200, 13), we get:

`\text{rate}=(13-25)/(2200-200)=(-12)/(2000)=-0.006`

So, the rate of change is -0.006

The rate of change shows that every time we add 1 meter to the altitude, the temperature will decrease 0.006 °C

Finally, the range of the graph is the set of all possible values that the temperature can take. So, the range is the set of numbers between 13 and 25°C