The population of the Philippines since 1975 is listed in the table below. }(c) Year 1975 treated as zero (x) & Population in millions (y) 0 & 41.3 5 & 47.4 10 & 54.3 15 & 61.9 20 & 69.6 25 & 77.6 Use a calculator to find the exponential regression equation for the data. Answer accurate to three decimal places. y=41.352(1.545)^x y=41.889(1.025)^x y=52.753(1.032)^x y=53.161(1.312)^x

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The population of the Philippines since 1975 is listed in the table below. }(c) Year 1975 treated as zero (x) & Population in millions (y) 0 & 41.3 5 & 47.4 10 & 54.3 15 & 61.9 20 & 69.6 25 & 77.6 Use a calculator to find the exponential regression equation for the data. Answer accurate to three decimal places. y=41.352(1.545)^x y=41.889(1.025)^x y=52.753(1.032)^x y=53.161(1.312)^x

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#Explanation The exponential regression equation is a mathematical model that attempts to fit data to an equation of the form \(y = ab^x\), where \(a\) and \(b\) are constants. This model is useful when the rate of change of a quantity is proportional to the quantity itself. Given the data, we can use a calculator with regression capabilities to find the best fit exponential regression equation. This is typically done using a method called least squares regression, which minimizes the sum of the squared differences between the actual and predicted values. The steps to do this on a calculator may vary depending on the model, but generally, you would: 1. Enter the data into the calculator's data table. 2. Choose the exponential regression option. 3. Perform the regression to find the values of \(a\) and \(b\). #Answer Without having the actual calculator to perform the regression, I cannot provide the correct answer. However, the correct answer would be one of the provided options.

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