To transform the function \( C(t) \), which represents the desert temperature in degrees Celsius, to a new function \( F(t) \) that represents the temperature in degrees Fahrenheit, follow these steps:
1. Apply the Conversion Formula:
The conversion rule from Celsius to Fahrenheit is given by:
[tex]\[
F(t) = \frac{9}{5} C(t) + 32
\][/tex]
2. Substitute \( C(t) \) into the Conversion Formula:
Suppose \( C(t) \) is a function representing the desert temperature in Celsius. To transform this function to Fahrenheit:
[tex]\[
F(t) = \frac{9}{5} C(t) + 32
\][/tex]
Each value of \( t \) (which could represent time or some other parameter in the function) that you plug into \( C(t) \) and then apply to the conversion formula will give you the corresponding temperature in Fahrenheit.
Therefore, the resulting function \( F(t) \) directly depends on the original Celsius function \( C(t) \):
[tex]\[
F(t) = \frac{9}{5} C(t) + 32
\][/tex]
In summary, the transformation involves multiplying the original function [tex]\( C(t) \)[/tex] by [tex]\(\frac{9}{5}\)[/tex] and then adding 32 to the result. This step-by-step transformation follows the conversion rule for converting temperatures from Celsius to Fahrenheit.
