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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A radioactive substance decays according to the formula W=20e^(-kt)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?