Answer:
Option 4 - [tex]F=[\frac{9}{5}\times C]+32[/tex]
Step-by-step explanation:
Given : John is going on a trip and the country he is traveling to uses the Celsius scale. He is curious about converting Celsius temperatures to Fahrenheit. John determines 68°F is equivalent to 20°C and 86°F is equivalent to 30°C.
To find : Which function models the relationship between Fahrenheit and Celsius?
Solution :
The conversion formula for a temperature that is expressed on the Celsius (C) scale to its Fahrenheit (F) is given by
[tex]F=[\frac{9}{5}\times C]+32[/tex]
For above model to be satisfied we put the values given and verify it,
1) John determines 68°F is equivalent to 20°C.
So, Put C= 20°C
[tex]F=[\frac{9}{5}\times 20]+32[/tex]
[tex]F=[9\times 4]+32[/tex]
[tex]F=36+32[/tex]
[tex]F=68[/tex]
Fahrenheit is 68°F verified.
2) John determines 86°F is equivalent to 30°C.
Now, Put C= 30°C
[tex]F=[\frac{9}{5}\times 30]+32[/tex]
[tex]F=[9\times 6]+32[/tex]
[tex]F=54+32[/tex]
[tex]F=86[/tex]
Fahrenheit is 86°F verified.
Therefore, Both the given condition is satisfied by the formula.
So, [tex]F=[\frac{9}{5}\times C]+32[/tex] function models the relationship between Fahrenheit and Celsius.
Hence, Option 4 is correct.
