Questions: Exponential Regression The table below shows the value, V, of an investment (in dollars) after n years. n 0 3 7 12 14 19 V 2900 3481.57 4656.77 6727.3 7477.75 9963.53 Use your calculator to determine the exponential regression equation that models the set of data above. Round the "a" value to two decimals, and round the "b" value to three decimals. Use the indicated variables. Based on your regression model, what is the percent increase per year? Use the rounded regression model from part 1 to find V when n=20. Round your answer to two decimal places. Interpret your answer by completing the following sentence. Be sure to use units in your answer. The value of the investment after 20 years

Exponential Regression
The table below shows the value, V, of an investment (in dollars) after n years.
n 0 3 7 12 14 19
V 2900 3481.57 4656.77 6727.3 7477.75 9963.53

Use your calculator to determine the exponential regression equation that models the set of data above. Round the "a" value to two decimals, and round the "b" value to three decimals. Use the indicated variables.

Based on your regression model, what is the percent increase per year?

Use the rounded regression model from part 1 to find V when n=20. Round your answer to two decimal places.

Interpret your answer by completing the following sentence. Be sure to use units in your answer. The value of the investment after 20 years
Transcript text: Exponential Regression The table below shows the value, $V$, of an investment (in dollars) after $n$ years. \begin{tabular}{|r|r|r|r|r|r|r|} \hline n & 0 & 3 & 7 & 12 & 14 & 19 \\ \hline V & 2900 & 3481.57 & 4656.77 & 6727.3 & 7477.75 & 9963.53 \\ \hline \end{tabular} Use your calculator to determine the exponential regression equation that models the set of data above. Round the "a" value to two decimals, and round the "b" value to three decimals. Use the indicated variables. Based on the your regression model, what is the percent increase per year? Use the rounded regression model from part 1 to find $V$ when $n=20$. Round your answer to two decimal places. Interpret your answer by completing the following sentence. Be sure to use units in your answer. The value of the investment after 20 years
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Solution

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Step 1: Data Collection

Collected data points: [(0, 2900), (3, 3481.57), (7, 4656.77), (12, 6727.3), (14, 7477.75), (19, 9963.53)]

Step 2: Exponential Regression Analysis

The exponential regression equation is $V(n) = 2998.44 \cdot 1.07^n$.

Step 3: Percent Increase Calculation

The percent increase per year is 6.61%.

Step 4: Future Value Prediction

The predicted value of the investment after 20 years is $10792.15.

Step 5: Time Required for Specific Value or Doubling

The time required for the investment to double is 10.82 years.

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