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The temperature of a metal, in °C, t minutes after it is heated is given by 72(1.2)'. Calculate the difference in temperature of the metal at 25th minute and 50th minute

User MindHacks
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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.

User He Shiming
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