Problem

Fill in the provided table for associated growth/decay rates and growth/decay factors. Recall that Factor $=1+$ Rate .

Complete the table below.
\begin{tabular}{|c|c|}
\hline Rate & Factor \\
\hline $2.86 \%$ & $\square$ \\
\hline$\square \%$ & 0.92 \\
\hline $0.06 \%$ & $\square$ \\
\hline$-15.6 \%$ & $\square$ \\
\hline$\square \%$ & 1.502 \\
\hline$\square \%$ & 0.48 \\
\hline
\end{tabular}
(Type integers or decimals.)

Answer

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Answer

\(\boxed{\text{Final Answer: The completed table is as follows:}}\) \begin{tabular}{|c|c|} \hline Rate & Factor \\ \hline 2.86% & 1.0286 \\ \hline -8.0% & 0.92 \\ \hline 0.06% & 1.0006 \\ \hline -15.6% & 0.844 \\ \hline 50.2% & 1.502 \\ \hline -52.0% & 0.48 \\ \hline \end{tabular}

Steps

Step 1 :Given the relationship between the rate and the factor as Factor = 1 + Rate, we can substitute the given rates into the equation and solve for the factor. Similarly, to find the missing rates, we can rearrange the equation to Rate = Factor - 1 and substitute the given factors into the equation.

Step 2 :For the first row, the rate is given as 2.86%. Substituting this into the equation gives Factor = 1 + 2.86% = 1.0286.

Step 3 :For the second row, the factor is given as 0.92. Rearranging the equation gives Rate = 0.92 - 1 = -8.0%.

Step 4 :For the third row, the rate is given as 0.06%. Substituting this into the equation gives Factor = 1 + 0.06% = 1.0006.

Step 5 :For the fourth row, the rate is given as -15.6%. Substituting this into the equation gives Factor = 1 - 15.6% = 0.844.

Step 6 :For the fifth row, the factor is given as 1.502. Rearranging the equation gives Rate = 1.502 - 1 = 50.2%.

Step 7 :For the sixth row, the factor is given as 0.48. Rearranging the equation gives Rate = 0.48 - 1 = -52.0%.

Step 8 :Thus, the completed table is as follows: \begin{tabular}{|c|c|} \hline Rate & Factor \\ \hline 2.86% & 1.0286 \\ \hline -8.0% & 0.92 \\ \hline 0.06% & 1.0006 \\ \hline -15.6% & 0.844 \\ \hline 50.2% & 1.502 \\ \hline -52.0% & 0.48 \\ \hline \end{tabular}

Step 9 :\(\boxed{\text{Final Answer: The completed table is as follows:}}\) \begin{tabular}{|c|c|} \hline Rate & Factor \\ \hline 2.86% & 1.0286 \\ \hline -8.0% & 0.92 \\ \hline 0.06% & 1.0006 \\ \hline -15.6% & 0.844 \\ \hline 50.2% & 1.502 \\ \hline -52.0% & 0.48 \\ \hline \end{tabular}

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