After a standard glucose load, a subject's blood glucose concentration follows the exponential decay model
$$ C(t)=C_{0}\,e^{-kt}+C_{\text{bas}} , $$
where $C_{\text{bas}}=5\ \text{mmol\ L}^{-1}$ is the basal concentration and $C_{0}$ is the excess above baseline at $t=0$. The measured concentration is 9 mmol L$^{-1}$ at $t=0$ and 7 mmol L$^{-1}$ at $t=30\ \text{min}$.
(i) Determine the decay constant $k$ (in $\text{min}^{-1}$).
(ii) Calculate the time (in minutes) required for the concentration to fall to within 0.2 mmol L$^{-1}$ of the basal level.

Question

After a standard glucose load, a subject's blood glucose concentration follows the exponential decay model  
$$ C(t)=C_{0}\,e^{-kt}+C_{\text{bas}} , $$  
where $C_{\text{bas}}=5\ \text{mmol\ L}^{-1}$ is the basal concentration and $C_{0}$ is the excess above baseline at $t=0$. The measured concentration is 9 mmol L$^{-1}$ at $t=0$ and 7 mmol L$^{-1}$ at $t=30\ \text{min}$.  
(i) Determine the decay constant $k$ (in $\text{min}^{-1}$).  
(ii) Calculate the time (in minutes) required for the concentration to fall to within 0.2 mmol L$^{-1}$ of the basal level.

Accepted Answer

k ≈ 0.0231 min⁻¹; time ≈ 130 min

Gce Model Questions Vol1 2023 Biology Question 7

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