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

pancha3

Answered question

2021-01-02

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.

Answer & Explanation

Nola Robson

Nola Robson

Skilled2021-01-03Added 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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