The half - life of a certain radioactive material is 85 days. An initial amount of the material has a mass of 801 kg Write an exponential function that models the decay of this material. Find how much radioactive material remains after 10 days. Round your answer to the nearest thousandth.

pancha3 2021-01-02 Answered
The half - life of a certain radioactive material is 85 days. An initial amount of the material has a mass of 801 kg Write an exponential function that models the decay of this material. Find how much radioactive material remains after 10 days. Round your answer to the nearest thousandth.
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Expert Answer

Nola Robson
Answered 2021-01-03 Author has 94 answers
Given initial mass:
m0=801kg at t=0
Let
m(t)=Mass at time t
The exponential function,
m(t)=m0ekt, where k =constant
Also given:
half life=85days
m(85)=m02
Now,
When t=85days:
m(85)=m0ek×85
m02=m0e85k
e85k=12
ek=(12)185
k=ln(12)185
k=185ln2
Therefore,
When t=10days:
m(10)=801ek×10
=801[e10×(185ln2}]
=738.273kg
Hence,
The radioactive material remains after 10 days =738.273kg
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