1. **Problem Statement:** We are given the amount of medication in the body over time $t$ hours during a 6-hour period, with the amount $a$ in mg. The data is: $$\begin{array}{c|c} \text{Time } t & \text{Amount } a \\ \hline 0 & 1500.0 \\ 1 & 1060.7 \\ 2 & 750 \\ 3 & 530.3 \\ 4 & 375.0 \\ 5 & 265.2 \\ 6 & 187.5 \end{array}$$ 2. **Goal:** Re-express the data pairs $(t,a)$ as $(t, \ln a)$ pairs, rounding each coordinate to two decimal places. 3. **Formula:** The natural logarithm function is $\ln a$, which transforms the amount $a$ to its logarithmic scale. 4. **Calculations:** Calculate $\ln a$ for each $a$: - $\ln 1500.0 = 7.31$ - $\ln 1060.7 \approx 6.97$ - $\ln 750 = 6.62$ - $\ln 530.3 \approx 6.27$ - $\ln 375.0 = 5.93$ - $\ln 265.2 \approx 5.58$ - $\ln 187.5 = 5.23$ 5. **Resulting pairs:** $$(0, 7.31), (1, 6.97), (2, 6.62), (3, 6.27), (4, 5.93), (5, 5.58), (6, 5.23)$$ These pairs represent the logarithm of the medication amount over time, useful for analyzing exponential decay.