A radioactive substance decays according to the formula #W=20e^(-kt)# grams where t is the time in hours. Find the rate of radioactive decay at : i) t=100 hours ii) t=1000 hours?

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Answer 1 · 2018-01-25T15:55:18

See the explanation below

The formula for the radioactive decay is

#W=20e^(-kt)#

To calculate the rate, differentiate with respect to #t#

#(dW)/dt=-20ke^(-kt)#

When #t=100h#

#(dW)/dt(t=100h)=-20ke^(-100k)gh^-1#

#=-20*0.0139e^(-0.0139*100)#

#=-0.0692gh^-1#

When #t=1000h#

#(dW)/dt(t=1000h)=-20ke^(-1000k)gh^-1#

#=-20*0.0139e^(-0.0139*1000)#

#=-0.0000003gh^-1#

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