Final answer:
The question likely refers to the half-lives of technetium-99 and thallium-201, which are used in medical imaging of heart muscles. After 2 days (48 hours), 0.391% of technetium-99's radioactivity and approximately 74.08% of thallium-201's radioactivity would remain.
Step-by-step explanation:
The question related to technetium and thallium appears to be asking about their respective half-lives and how they would relate to filter coefficients in medical imaging, particularly in the context of heart muscle imaging in patients with suspected heart problems. However, 'filter coefficients' typically are more related to signal processing than nuclear medicine, so there might be some confusion here.
Instead, if we are to discuss the decay of these isotopes, technetium-99 has a half-life of 6 hours, and thallium-201 has a half-life of 73 hours. To calculate the remaining percentage of radioactivity after 2 days (48 hours), we need to use the formula for exponential decay:
Remaining percentage (%) = 100 * (1/2)^(elapsed time in hours/half-life)
For technetium-99: Remaining percentage = 100 * (1/2)^(48/6) = 100 * (1/2)^8 = 100 * 0.00391 = 0.391%
For thallium-201: Remaining percentage = 100 * (1/2)^(48/73) ≈ 100 * (1/2)^(0.6575) ≈ 100 * 0.74082 ≈ 74.08%