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Question

The mass of a radioactive substance follows a continuous exponential decay model. A sample of this radioactive substance has an initial mass of 1193 kg and decreases continuously at a relative rate of 3% per day. Find the mass of the sample after two days. Do not round any intermediate computations, and round your answer to the nearest tenth.

Answer 1

1193(1-.03)^2

= 1193(.97)^2

=1193(.9409)

= 1122.49 kg after 2 days

97% remaining after one day

94.09% remaining after two days

but for continous decay, use an exponential function

A =Pe^rt where r=percentage decay rate per day and t = number of days, e= about 2.718

A = 1193e^-.03(2)

= 1193(e^-.06)

1193(.9418)

= 1123.53 kg after 2 days

94.18% remaining after 2 days

the difference is similar to interest compounded continuously or compounded daily,

with a negative interest rate