Answer :
To determine which function models the relationship between Fahrenheit (F) and Celsius (C), we need to verify which formula correctly converts Celsius temperatures to Fahrenheit. We have two formulas to test:
1. [tex]\( F = \frac{5}{9} C - \frac{512}{9} \)[/tex]
2. [tex]\( F = \frac{9}{5} C + 32 \)[/tex]
Given conversion pairs are:
- [tex]\( 20^\circ C = 68^\circ F \)[/tex]
- [tex]\( 30^\circ C = 86^\circ F \)[/tex]
Let's test both formulas with these known pairs:
### Check the first set:
1. For [tex]\( C = 20 \)[/tex]:
- Using [tex]\( F = \frac{5}{9} C - \frac{512}{9} \)[/tex]:
- Plugging in the value: [tex]\( F = \frac{5}{9} \times 20 - \frac{512}{9} \approx -45.78 \)[/tex] (This does not match 68 degrees)
- Using [tex]\( F = \frac{9}{5} C + 32 \)[/tex]:
- Plugging in the value: [tex]\( F = \frac{9}{5} \times 20 + 32 = 68 \)[/tex] (This matches the given Fahrenheit temperature)
### Check the second set:
2. For [tex]\( C = 30 \)[/tex]:
- Using [tex]\( F = \frac{5}{9} C - \frac{512}{9} \)[/tex]:
- Plugging in the value: [tex]\( F = \frac{5}{9} \times 30 - \frac{512}{9} \approx -40.22 \)[/tex] (This does not match 86 degrees)
- Using [tex]\( F = \frac{9}{5} C + 32 \)[/tex]:
- Plugging in the value: [tex]\( F = \frac{9}{5} \times 30 + 32 = 86 \)[/tex] (This matches the given Fahrenheit temperature)
### Conclusion:
The second formula, [tex]\( F = \frac{9}{5} C + 32 \)[/tex], consistently provides the correct F values for the given C values. Therefore, this is the correct function to model the relationship between Fahrenheit and Celsius.
1. [tex]\( F = \frac{5}{9} C - \frac{512}{9} \)[/tex]
2. [tex]\( F = \frac{9}{5} C + 32 \)[/tex]
Given conversion pairs are:
- [tex]\( 20^\circ C = 68^\circ F \)[/tex]
- [tex]\( 30^\circ C = 86^\circ F \)[/tex]
Let's test both formulas with these known pairs:
### Check the first set:
1. For [tex]\( C = 20 \)[/tex]:
- Using [tex]\( F = \frac{5}{9} C - \frac{512}{9} \)[/tex]:
- Plugging in the value: [tex]\( F = \frac{5}{9} \times 20 - \frac{512}{9} \approx -45.78 \)[/tex] (This does not match 68 degrees)
- Using [tex]\( F = \frac{9}{5} C + 32 \)[/tex]:
- Plugging in the value: [tex]\( F = \frac{9}{5} \times 20 + 32 = 68 \)[/tex] (This matches the given Fahrenheit temperature)
### Check the second set:
2. For [tex]\( C = 30 \)[/tex]:
- Using [tex]\( F = \frac{5}{9} C - \frac{512}{9} \)[/tex]:
- Plugging in the value: [tex]\( F = \frac{5}{9} \times 30 - \frac{512}{9} \approx -40.22 \)[/tex] (This does not match 86 degrees)
- Using [tex]\( F = \frac{9}{5} C + 32 \)[/tex]:
- Plugging in the value: [tex]\( F = \frac{9}{5} \times 30 + 32 = 86 \)[/tex] (This matches the given Fahrenheit temperature)
### Conclusion:
The second formula, [tex]\( F = \frac{9}{5} C + 32 \)[/tex], consistently provides the correct F values for the given C values. Therefore, this is the correct function to model the relationship between Fahrenheit and Celsius.
