Problem

An experiment is run. The mass of an object is recorded over time. \begin{tabular}{|r|r|} \hline Time (min) & Mass (g) \\ \hline 11 & 47 \\ \hline 17 & 37 \\ \hline 35 & 27 \\ \hline 40 & 17 \\ \hline 47 & 14 \\ \hline \end{tabular} Clear All Draw: Dot Using your calculator, run a linear regression to determine the equation of the line of best fit. Round to two decimal places, use $x$ for the variable. $y=$ Using your equation, estimate the mass of the object at 50 minutes. grams

Solution

Step 1 :Given data points:\begin{tabular}{|r|r|} \hline Time (min) & Mass (g) \\ \hline 11 & 47 \\ \hline 17 & 37 \\ \hline 35 & 27 \\ \hline 40 & 17 \\ \hline 47 & 14 \\ \hline \end{tabular}

Step 2 :Run a linear regression to determine the equation of the line of best fit, rounding to two decimal places: \(y = -0.98x + 58.15\)

Step 3 :Use the equation to estimate the mass of the object at 50 minutes: \(y = -0.98(50) + 58.15\)

Step 4 :Calculate the estimated mass: \(y = 10.79\)

Step 5 :\(\boxed{\text{The estimated mass of the object at 50 minutes is approximately 10.79 grams}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/17060/

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