Question

The heat index is calculated using the relative humidity and the temperature. for every 1 degree increase in the temperature from 94∘F to 98∘F at 75% relative humidity the heat index rises 4∘F. on a summer day the relative humidity is 75% the temperature is 94 ∘F and the heat index is 122f. Construct a table that relates the temperature t to the Heat Index H. a. Construct a table at 94∘F and end it at 98∘F. b. Identify the independent and dependent variables. c. Write a linear function that represents this situation. d. Estimate the Heat Index when the temperature is 100∘F.

Answer 1

To construct a table that relates the temperature t to the Heat Index H, we can use the given information: for every 1 degree increase in the temperature from 94°F to 98°F at 75% relative humidity, the heat index rises 4°F.

Step-by-step explanation:

To construct a table that relates the temperature t to the Heat Index H, we can use the given information: for every 1 degree increase in the temperature from 94°F to 98°F at 75% relative humidity, the heat index rises 4°F.

Here is the table:

Temperature (°F)Heat Index (°F)9412295126961309713498138

The independent variable is the temperature (t), and the dependent variable is the Heat Index (H). We can write a linear function to represent this situation:

H = 4(t - 94) + 122

To estimate the Heat Index when the temperature is 100°F, we can substitute t = 100 into the linear function:

H = 4(100 - 94) + 122 = 148°F

Answer 2

A table relating temperature to the Heat Index at 75% humidity shows a linear increase of 4°F in the Heat Index for every 1°F rise in temperature from 94°F to 98°F. The linear function describing this relationship is H(t) = 4t + 66. Using this function, the estimated Heat Index at 100°F is calculated to be 466°F.

Step-by-step explanation:

To construct a table that relates temperature (t) to the Heat Index (H) given that on a day with 75% humidity, for every 1 degree increase in temperature from 94°F to 98°F, the heat index rises by 4°F, we start with an initial temperature of 94°F and a heat index of 122°F.

t = 94°F, H = 122°F

t = 95°F, H = 126°F

t = 96°F, H = 130°F

t = 97°F, H = 134°F

t = 98°F, H = 138°FIn this scenario, the independent variable is the temperature (t), and the dependent variable is the Heat Index (H). We can represent the linear relationship between the temperature and the Heat Index by the function H(t) = 4t + 66, where 't' is the temperature in degrees Fahrenheit starting from 94°F.

To estimate the Heat Index when the temperature is 100°F, we can substitute t = 100 into the function:

H(100) = 4(100) + 66 = 400 + 66 = 466°F.

Therefore, the estimated Heat Index at 100°F with 75% humidity would be 466°F.