Question

a cup of soup is left on a countertop to cool. the table below gives the temperatures, in degrees fahrenheit, of the soup recorded over a 10 - minute period.
write an exponential regression equation for the data, rounding all values to the nearest thousandth.

Explanation:

Step1: Input data into calculator

Input the \(x\) (time) and \(y\) (temperature) values from the table into a graphing calculator or statistical software that can perform exponential regression.

Step2: Obtain exponential regression equation

Using the exponential regression function \(y = ab^{x}\), after calculation, we get \(a\approx180.197\) and \(b\approx0.939\)

Answer:

\(y = 180.200\times0.939^{x}\)