Answer to Question #241330 in Calculus for Faiq

Question #241330

The radioactive isotope gallium-67, used in the diagnosis of malignant tumors, has a biological

𝑑


half-life of 46.5 hours. The half-life of the isotope is modeled as 𝐴 = 𝐴0 (12)β„Ž , where h is the half-life and t is the time in hours. If we start with 100 milligrams of the isotope, how many milligrams will be left after: 24 hours, and after 1 week? 


1
Expert's answer
2021-09-24T16:03:01-0400

t1/2=46.5hrs

A=Ao(2)βˆ’thA=A_o(2)^{-\frac{t}{h}}

Ao=100mg

h=46.5hrs

t=24hrs

A=100(2)βˆ’24hrs46.5hrsA=100(2)^{-\frac{24hrs}{46.5hrs}}

=69.92mg left after 24hours

Given t=1week=24*7=168hours

A=100(2)βˆ’16846.5A=100(2)^{-\frac{168}{46.5}}

=8.17mg left after one week.


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