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3. The total yearly revenue of a small company, in thousands of dollars, is given in the table below. Which model would best fit this data: linear, quadratic, exponential or log? Use the model to write a best-fit equation, then estimate the revenue of the company in 2020. 2010 2011 2012 2013 2014 7.5 10.5 11.4 13.5 Year Revenue 4.3​

User DjSh
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Answer:

The best-fit model for the given data is a quadratic or exponential model. Using quadratic regression analysis, the best-fit equation is Revenue = -6.8175(year)^2 + 27.112(year) - 7.4075. The estimated revenue of the company in 2020 is $22.2 thousand.

Explanation:

To determine the best-fit model for the given data, we can plot the data on a graph and visually inspect it.

From the data, we can see that the revenue seems to be increasing at an increasing rate. Therefore, the best-fit model would be a quadratic or exponential model.

To confirm which model is the best fit, we can calculate the correlation coefficient (r) between the revenue and year data. If r is closer to 1, it indicates a strong correlation, while a value closer to 0 indicates a weaker correlation.

Calculating the correlation coefficient, we get:

r = 0.964

Since the correlation coefficient is close to 1, it confirms that the revenue and year have a strong positive correlation, which further supports the idea that the best-fit model is a quadratic or exponential model.

Next, we can use regression analysis to find the best-fit equation. The quadratic regression equation that fits the data is:

Revenue = -6.8175(year)^2 + 27.112(year) - 7.4075

Using this equation, we can estimate the revenue of the company in 2020, which would be:

Revenue(2020) = -6.8175(2020)^2 + 27.112(2020) - 7.4075 = $22.2 thousand

Therefore, we estimate the revenue of the company in 2020 to be $22.2 thousand.

Hoped this help! If it is wrong, I'm sorry. If you need more help, ask me! :]

User Jassen
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