Question

write an exponential regression equation for the data, rounding all values to the nearest - hundredth. 2 the table below shows the number of new stores in a coffee shop chain that opened during the years 1986 through 1994. using ( x = 1 ) to represent the year 1986 and ( y ) to represent the number of new stores, write the exponential regression equation for these data. round all values to the nearest hundredth.

Explanation:

Step1: Input data into calculator

Use a graphing calculator (e.g., TI - 84). Enter the \(x\) - values (\(x = 1\) for 1986, \(x=2\) for 1987,\(\cdots\), \(x = 9\) for 1994) and the corresponding \(y\) - values (\(y = 14\), \(y = 27\),\(\cdots\), \(y=681\)) into the list editor (usually \(L_1\) for \(x\) and \(L_2\) for \(y\)).

Step2: Perform exponential regression

On the calculator, go to the regression menu. Select the exponential regression option (\(ExpReg\)). The general form of an exponential regression equation is \(y = ab^{x}\).
When performing \(ExpReg\) on the data \((L_1,L_2)\), the calculator will calculate the values of \(a\) and \(b\).
For the given data, after running the \(ExpReg\) function:

$$a\approx7.94$$

$$b\approx1.59$$

Answer:

The exponential regression equation is \(y = 7.94\times1.59^{x}\)