An isotope of a radioactive element has decay constant equal to 0.06 per year.Initially, there are 3 million atoms of the isotope present.Since the isotope decays exponentially, the number of atoms obeys the following equationP=3e^-0.06tIn this question, time is measured in years and the number of atoms, P, is measured in millions. What is the value of the decay constant?Decay constant : ___ per year. What is the half-life of the isotope?(Enter your answer correct to two decimal places.)Half-life : ___years. How many million atoms will be present after 7 years have passed?(Enter your answer correct to one decimal place.)Number present after 7 years : ___ million.

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Answered: An isotope of a radioactive element has…

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Chapter6: Vector Spaces

Section6.7: Applications

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An isotope of a radioactive element has decay constant equal to 0.06 per year.

Initially, there are 3 million atoms of the isotope present.

Since the isotope decays exponentially, the number of atoms obeys the following equation

P=3e^-0.06t

In this question, time is measured in years and the number of atoms, P, is measured in millions.

What is the value of the decay constant?
Decay constant : ___ per year.
What is the half-life of the isotope?
(Enter your answer correct to two decimal places.)

Half-life : ___years.
How many million atoms will be present after 7 years have passed?
(Enter your answer correct to one decimal place.)

Number present after 7 years : ___ million.

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