Question

the following situation involves a rate of change that is constant. write a statement that describes how one variable changes with - respect to the other, give the rate of change numerically (with units), and use the rate of change rule to answer any questions. a 1 - degree change (increase or decrease) on the celsius temperature scale is equivalent to a $\frac{9}{5}$ - degree change on the fahrenheit temperature scale. how much does the fahrenheit temperature increase if the celsius temperature increases 9 degrees? how much does the fahrenheit temperature decrease if the celsius temperature decreases 25 degrees? a. the celsius temperature varies with respect to the fahrenheit temperature with a rate of change of $\frac{9}{5}$°f per degree c. b. the fahrenheit temperature varies with respect to the celsius temperature with a rate of change of $\frac{9}{5}$°c per degree f. c. the celsius temperature varies with respect to the fahrenheit temperature with a rate of change of $\frac{9}{5}$°c per degree f. d. the fahrenheit temperature varies with respect to the celsius temperature with a rate of change of $\frac{9}{5}$°f per degree c. what is the increase in fahrenheit temperature if the celsius temperature increases by 9°? 16.2°f (type an integer or a decimal.) what is the decrease in fahrenheit temperature if the celsius temperature decreases by 25°? °f (type an integer or a decimal.)

Explanation:

Step1: Identify the rate - of - change

We know that a 1 - degree change on the Celsius temperature scale is equivalent to a $\frac{9}{5}$ degree change on the Fahrenheit temperature scale. So the Fahrenheit temperature varies with respect to the Celsius temperature with a rate of change of $\frac{9}{5}$°F per degree C.

Step2: Calculate increase in Fahrenheit for 9 - degree Celsius increase

If the rate of change is $\frac{9}{5}$°F per degree C and the Celsius temperature increases by 9 degrees, then the increase in Fahrenheit is $\text{Increase in }F=\frac{9}{5}\times9=\frac{81}{5} = 16.2$°F.

Step3: Calculate decrease in Fahrenheit for 25 - degree Celsius decrease

If the rate of change is $\frac{9}{5}$°F per degree C and the Celsius temperature decreases by 25 degrees, then the decrease in Fahrenheit is $\text{Decrease in }F=\frac{9}{5}\times25=45$°F.

Answer:

D. The Fahrenheit temperature varies with respect to the Celsius temperature with a rate of change of $\frac{9}{5}$°F per degree C
16.2
45