Question
Half-life of HIV Use the graph of $V$ in Figure 12 to estimate the half-life of the viral load of patient 303 during the first month of treatment.
Step 1
From the graph, we can see that at time $t=1$ (the first day of treatment), the viral load $V$ is 76. Show more…
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Use the graph of $ V $ in Figure 11 to estimate the half-life of the viral load of patient 303 during the first month of treatment.
Functions and Models
Exponential Functions
The table shows values of the viral load $V(t)$ in HIV patient $303,$ measured in RNA copies $/ \mathrm{mL}, t$ days after ABT-538 treatment was begun. $$\begin{array}{|c|c|c|c|c|c|} \hline t & 4 & 8 & 11 & 15 & 22 \\ \hline V(t) & 53 & 18 & 9.4 & 5.2 & 3.6 \\ \hline \end{array}$$ (a) Find the average rate of change of $V$ with respect to $t$ over each time interval: (i) [4,11] (ii) [8,11] (iii) [11,15] (iv) [11,22] What are the units? (b) Estimate and interpret the value of the derivative $V^{\prime}(11)$.
Derivatives
Derivatives and Rates of Change
The table shows values of the viral load $ V(t) $ in HIV patient 303, measured in RNA copies/mL, $ t $ days after ABT-538 treatment was begun. (a) Find the average rate of change of $ V $ with respect to $ t $ over each time interval: (i) $ [4, 11] $ (ii) $ [8, 11] $ (iii) $ [11, 15] $ (iv) $ [11, 22] $ What are the units? (b) Estimate and interpret the value of the derivative $ V'(11) $.
Limits and Derivatives
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