The difference in temperature between the 25th and 50th minutes is approximately 46,654,115.44 °C.
1. Calculate the temperatures at the 25th and 50th minutes:
The temperature of the metal at any minute t is given by the formula:
T(t) = 72 * (1.2)^t
Temperature at 25th minute (T25):
T25 = 72 * (1.2)^25
Temperature at 50th minute (T50):
T50 = 72 * (1.2)^50
2. Calculate the difference in temperature:
To find the difference in temperature between the 25th and 50th minutes, simply subtract T25 from T50:
Difference in temperature = T50 - T25
3. Solve the equation:
Substitute the formulas for T25 and T50:
Difference in temperature = [72 * (1.2)^50] - [72 * (1.2)^25]
Factor out the common term:
Difference in temperature = 72 * (1.2)^25 * [(1.2)^25 - 1]
4. Calculate the result:
(1.2)^25 is a large number, so subtracting 1 from it won't significantly affect the answer. Therefore, you can approximate:
Difference in temperature ≈ 72 * (1.2)^25 * (1.2)^25
Difference in temperature ≈ 72 * (1.2)^50
Calculating the exact value of (1.2)^50 is computationally expensive, but you can round it to a few significant figures depending on the required accuracy. For example, rounding to 3 decimal places:
Difference in temperature ≈ 72 * 648363.02 ≈ 46654115.44 °C
Therefore, the difference in temperature between the 25th and 50th minutes is approximately 46,654,115.44 °C. This indicates a significant increase in temperature during that period.