Exponentially Cool

Algebra Level pending

A metal alloy when it is removed from the smelter has a temperature of 3000°C and its temperature reduces at rate of 1% every 30 minutes. Approximately, how long does the temperature of this metal alloy become only 30°C (in hours)?

Details and Assumptions: use log ⁡ ( 3 ) = 0.477 \log(3)=0.477 and log ⁡ ( 11 ) = 1.041 \log(11)=1.041 .

50 Hours 400 Hours 200 Hours 22 Hours 100 Hours

Victor Paes Plinio by Victor Paes Plinio , 21, Brazil

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1 solution

The exponential formula for this problem is N = 3000 x 0.99^t. So we are looking for 30 = 3000 x 0.99^t. This leads to log(0.01) = t x log(.0.99). So t = log(0.01)/log(0.99)

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