To find the half-life of the element, we need to find the value of t when A(t) is equal to half of A0.
A(t) = A0e^(-0.0303t)
Setting A(t) = (1/2)A0:
(1/2)A0 = A0e^(-0.0303t)
Dividing both sides by A0:
(1/2) = e^(-0.0303t)
Taking the natural logarithm of both sides:
ln(1/2) = -0.0303t
Using a calculator to approximate ln(1/2) ≈ -0.693:
-0.693 = -0.0303t
Dividing both sides by -0.0303:
t ≈ 22.88
Therefore, the half-life of the radioactive element is approximately 22.9 years.
Find the half-life of a radioactive element, which decays according to the function A(t)=A0e−0.0303t, where t is the time in years.
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Part 1
The half-life of the element is
enter your response here years.
(Round to the nearest tenth.)
1 answer