The table that follows shows the relationship between the boiling temperature of water (°F) and the altitude (per thousand feet):
Boiling Point of Water
Altitude
(1000 ft.) Temperature
(°F)
8 197.6
4.5 203.9
3 206.6
2.5 207.5
Gemma and Tessa need to find the rate of change for the data in the previous table. A. Gemma’s first steps are +6.3/-3.5 Which two ordered pairs did Gemma use to set up her
Tessa’s first steps are +0.9/-0.5 Which two ordered pairs did Tessa use to set up her ratio?
To find the rate of change, both Gemma and Tessa need to determine the difference in the temperature values (ΔTemperature) and the difference in the altitude values (ΔAltitude) for the two ordered pairs they choose.
For Gemma:
Gemma's first steps are +6.3/-3.5, which means she used the ratio of ΔTemperature/ΔAltitude = 6.3/(-3.5).
To determine the two ordered pairs she used, we need to find two sets of data points with a difference in altitude of 3.5.
Looking at the table, we see that the altitude difference of 3.5 occurs between the 8 ft. and 4.5 ft. altitude points. Therefore, her two ordered pairs are (8, 197.6) and (4.5, 203.9).
For Tessa:
Tessa's first steps are +0.9/-0.5, which means she used the ratio of ΔTemperature/ΔAltitude = 0.9/(-0.5).
To determine the two ordered pairs she used, we need to find two sets of data points with a difference in altitude of 0.5.
Looking at the table, we see that the altitude difference of 0.5 occurs between the 4.5 ft. and 3 ft. altitude points. Therefore, her two ordered pairs are (4.5, 203.9) and (3, 206.6).
So, Gemma used the ordered pairs (8, 197.6) and (4.5, 203.9), while Tessa used the ordered pairs (4.5, 203.9) and (3, 206.6) to set up their respective ratios.