Medicine core problems

Problem 1 – Drug resonance half-life#

A drug’s half-life is modeled as

$$ t_{1/2} = \frac{\ln 2}{ΛΘ}. $$

If $$Θ$$ decreases by 10%, how does $$t_{1/2}$$ change?

Problem 2 – Heart rhythm resonance#

Heart rhythm is modeled as

$$ R = T_f D_3. $$

If $$T_f$$ increases by 8%, what is the percent change in $$R$$?

Problem 3 – Dose-response resonance#

A dose-response curve is modeled as

$$ S = \frac{X}{1 + e^{-τ_r}}. $$

If $$τ_r$$ increases, how does the response $$S$$ change qualitatively?