Question

4 the table below shows the concentration of ozone in earths atmosphere at different altitudes. write the exponential regression equation that models these data, rounding all values to the nearest thousandth.

Explanation:

Step1: Input data into calculator

Input the \(x\) (altitude) and \(y\) (ozone units) values into a graphing calculator or statistical software.

Step2: Perform exponential regression

Use the exponential regression function (\(y = ab^{x}\)) on the calculator. For a TI - 84 Plus, press STAT, then EDIT to enter the data. Then press STAT, arrow over to CALC, and select ExpReg.
When we perform the exponential regression on the data \((x_1 = 0,y_1=0.7)\), \((x_2 = 5,y_2 = 0.6)\), \((x_3=10,y_3 = 1.1)\), \((x_4 = 15,y_4=3.0)\), \((x_5=20,y_5 = 4.9)\):
The general form of an exponential regression equation is \(y=ab^{x}\).
The calculator will output values for \(a\) and \(b\). After performing the regression:
\(a\approx0.797\) and \(b\approx1.047\)

Answer:

\(y = 0.797\times(1.047)^{x}\)