Let's solve the problem step-by-step:
1. Given: Initial Temperature
Let's assume the initial temperature is \( T_0 = 100 \) units.
2. First Change: Increase by 25%
To find the temperature after increasing by 25%, we'll calculate:
[tex]\[
T_1 = T_0 + (0.25 \times T_0)
\][/tex]
Alternatively, we can use:
[tex]\[
T_1 = T_0 \times (1 + 0.25)
\][/tex]
Substituting the initial temperature \( T_0 = 100 \):
[tex]\[
T_1 = 100 \times 1.25 = 125
\][/tex]
So, the temperature after the first change is 125 units.
3. Second Change: Decrease by 40%
Next, we need to decrease this new temperature by 40%. To calculate this:
[tex]\[
T_2 = T_1 - (0.4 \times T_1)
\][/tex]
Alternatively, we can use:
[tex]\[
T_2 = T_1 \times (1 - 0.40)
\][/tex]
Substituting the intermediate temperature \( T_1 = 125 \):
[tex]\[
T_2 = 125 \times 0.60 = 75
\][/tex]
So, the temperature after the second change is 75 units.
4. Total Change in Temperature
The total change in temperature from the initial value \( T_0 \) to the final value \( T_2 \) is:
[tex]\[
\Delta T = T_2 - T_0
\][/tex]
Substituting \( T_0 = 100 \) and \( T_2 = 75 \):
[tex]\[
\Delta T = 75 - 100 = -25
\][/tex]
So, the temperature initially increased to 125 units, then decreased to 75 units, resulting in an overall temperature change of [tex]\(-25\)[/tex] units.
