Choose the one alternative that best completes the statement or answers the question.
-After introducing an inhibitor into a culture of luminescent bacteria, a scientist monitors the luminosity produced by the culture. Use a graphing utility to fit a logarithmic function to the data. Predict the luminosity after 20 hours.
$\begin{array}{l|ccccccc}
\text { Time, hrs } & 2 & 3 & 4 & 5 & 8 & 10 & 15 \
\hline \text { Luminosity } & 77.4 & 60.8 & 54.5 & 45.8 & 30.0 & 24.3 & 10.5
\end{array}$

A) $y = 98.75 - 32.66 \ln ( \mathrm { x } ) , 0.91$
B) $y = 107.55 - 41 \ln ( x ) , - 15.27$
C) $\mathrm { y } = 112.97 - 45.97 \ln ( \mathrm { x } ) , - 24.74$
D) $y = 100.5 - 32.7 \ln ( x ) , 2.54$

Question

Choose the one alternative that best completes the statement or answers the question.
-After introducing an inhibitor into a culture of luminescent bacteria, a scientist monitors the luminosity produced by the culture. Use a graphing utility to fit a logarithmic function to the data. Predict the luminosity after 20 hours.
$\begin{array}{l|ccccccc}
\text { Time, hrs } & 2 & 3 & 4 & 5 & 8 & 10 & 15 \
\hline \text { Luminosity } & 77.4 & 60.8 & 54.5 & 45.8 & 30.0 & 24.3 & 10.5
\end{array}$

A) $y = 98.75 - 32.66 \ln ( \mathrm { x } ) , 0.91$
B) $y = 107.55 - 41 \ln ( x ) , - 15.27$
C) $\mathrm { y } = 112.97 - 45.97 \ln ( \mathrm { x } ) , - 24.74$
D) $y = 100.5 - 32.7 \ln ( x ) , 2.54$

Quizplus · Accepted Answer

The correct choice is determined by fitting a logarithmic function to the given data points. Among the options, choice A provides a logarithmic function that could reasonably fit the trend of decreasing luminosity over time, as indicated by the data. The other options either have coefficients that don't align as well with the general trend of the data or include values not relevant to the function's form (e.g., an extra number outside the function). Logarithmic functions are often used to model phenomena that decrease rapidly at first and then level off, which seems to match the description of the luminosity decrease in the bacteria culture.

Choose the One Alternative That Best Completes the Statement or Answers