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allochka39001 [22]
3 years ago
6

How long will it take a sample of radioactive substance to decay to half of its original amount, if it decays according to the f

unction A(t) = 350e-0.169t, where t is the time in years? Round your answer to the nearest hundredth year.
Mathematics
1 answer:
crimeas [40]3 years ago
5 0

Answer:

4.101 yrs

Step-by-step explanation:

Given that a sample of radioactive substance to decay has the following exponential function.

A(t)=350e^{-0.169t}

where t= no of years lapsed

When t=0 i.e. initially we have population as

A(0) = 350

When it becomes half we have

=A(t) = 175 =  350e^{-0.169t}\\0.5= e^{-0.169t}\\

Taking log to base e we have

-0.169t = ln (0.5) \\t=4.101

In approximately 4.101 years the population decays to half

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