A bar of metal is cooling from 1000°C to room temperature, 22°C. The temperature, H, of the bar t minutes after it starts cooling is given, in °C, by H = 22 + 978e-0.1t.

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Mathematics

Allan Morse

4 February, 03:26

A bar of metal is cooling from 1000°C to room temperature, 22°C. The temperature, H, of the bar t minutes after it starts cooling is given, in °C, by H = 22 + 978e-0.1t.

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Krish Fox · Answer 1

I assume you're looking for a time-weighed average rather than just the [H (0) + H (60) ]/2 average.

Havg = (1/60) â"[20+980e^ (-0.1t) ]dt (evaluated from 0 to 60)

Havg = (1/60) [20t - 98e^ (-0.1t) ] evaluated from 0 to 60

Havg = (1/60) [20 (60) - 98e^ (-6) - 20 (0) + 98e^ (0) ] = 1297.76/60 = 21.629 Â°C