We will investigate an example regarding temperature data given and initial temperature and the rate at which the temperature increases or decreases.
The initial temperature given to us is as follows:
![T_i\text{ = -25 degrees}](https://img.qammunity.org/2023/formulas/mathematics/college/g8g7u32ogulfrzk5epad2cwsojf264pkox.png)
The rate at which the temperature decreases/increases is:
![r\text{ = }T_f-T_i](https://img.qammunity.org/2023/formulas/mathematics/college/ty7kvmay6rmfmok3nqjajkrvnlvtzko214.png)
We are given that the temeperature decreases by a certain amount ( r ) as follows:
![r\text{ = -15 degrees}](https://img.qammunity.org/2023/formulas/mathematics/college/aiw19g628uxslz4y78l50vb6h807rm7n8n.png)
We will use the definition of rate ( r ) expressed as an equation and determine the final temperature for the given:
![T_i=-25,r=-15,T_f\text{ = ?}](https://img.qammunity.org/2023/formulas/mathematics/college/wwgjick5nwvqsyfy786p2e9wuculwxeetf.png)
Plug in the respective values in the expression defined and evaluate the final temperature:
![\begin{gathered} -15\text{ = }T_f\text{ - (-}25\text{ )} \\ -15\text{ = }T_f+\text{ 25} \\ T_f\text{ = -15 - 25} \\ T_f\text{ = -30} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/5t6go0r3bf8x51kofxfsasrngs8hlurlp0.png)