When the temperature is 0 degrees Celsius, the Fahrenheit temperature is 32 degrees. When the Celsius temperature is 100 degrees, the corresponding Fahrenheit temperature is 212 degrees. Express the Fahrenheit temperature as a linear function of C, the Celsius temperature, \( F(C) \).

a) Find the rate of change of Fahrenheit temperature for each unit change in Celsius temperature.

b) Find and interpret \( F(28) \).

c) Find and interpret \( F(-40) \).

The Fahrenheit temperature as a linear function of the Celsius temperature is given by F(C) = (9/5)C + 32. The rate of change is 1.8 degrees Fahrenheit for each degree Celsius. At 28 degrees Celsius, the Fahrenheit temperature is 82.4 degrees, and at -40 degrees, the two scales coincide at -40 degrees.

Explanation:

To express the Fahrenheit temperature as a linear function of Celsius temperature, we use the formula F(C) = (9/5)C + 32, which relates Fahrenheit (F) to Celsius (C).

a) Rate of change of Fahrenheit temperature per unit change in Celsius

The rate of change is given by the coefficient of C in the linear function, which is 9/5. Therefore, for each one degree Celsius change, the Fahrenheit temperature changes by 1.8 degrees Fahrenheit.

b) Interpret F(28)

F(28) would be the Fahrenheit temperature corresponding to 28 degrees Celsius. To find this, we plug 28 into the formula: F(28) = (9/5)*28 + 32, which gives us 82.4 degrees Fahrenheit. This means that 28 degrees Celsius is equivalent to 82.4 degrees Fahrenheit.

c) Interpret F(-40)

F(-40) is interesting because it's the point where Celsius and Fahrenheit scales coincide.

Calculating F(-40) = (9/5)*(-40) + 32 confirms that -40 degrees Celsius is equal to -40 degrees Fahrenheit.