Answer to Question #241330 in Calculus for Faiq

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 (¹₂)^ℎ , 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? 

Answer 1

t_1/2=46.5hrs

$A=A_o(2)^{-\frac{t}{h}}$

A_o=100mg

h=46.5hrs

t=24hrs

$A=100(2)^{-\frac{24hrs}{46.5hrs}}$

=69.92mg left after 24hours

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

$A=100(2)^{-\frac{168}{46.5}}$

=8.17mg left after one week.