Molecules of a toxic chemical eventually decompose into inert substances. Suppose the decomposition time is exponentially distributed with a mean of 1/lambda. The half-life of such a persistent poison is that time beyond which the probability is .50 that a particular molecule will remain toxic. Find the half-life for chemicals whose molecules have an average decomposition time of

a)4.15 years

b)22.18 years

c)188.53 years

d)3027.66 years

Step-by-step explanation:

Formula :

So,

We are given that The half-life of such a persistent poison is that time beyond which the probability is .50 that a particular molecule will remain toxic i.e. P(X>t)=0.5

So,

Taking natural log both sides

a)

t=-(6) ln(0.5)=4.15 years

b)

t=-(32) ln(0.5)=22.18 years

c)

t=-(272) ln(0.5)=188.53 years

d)

t=-(4368) ln(0.5)=3027.66 years

step-by-step explanation: