Answer to Question #241793 in Algebra for Tina

Question

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

𝑡

half-life of 46.5 hours. The half-life of the isotope is modeled as 𝐴 = 𝐴0 (1)h , where h is the 2

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?

Answer 1

$A=A_0(2)^{-\frac{t}{h}}\\ A_0=100mg,~~h=46.5 hrs\\ A=100(2)^{-\frac{t}{46.5}}\\ \text{After 24hrs}\\ A=100(2)^{-\frac{24}{46.5}}=53.379mg\\ \text{After 1 weeks}\\ A=100(2)^{-\frac{24\times 7}{46.5}}=1.235mg$