Question

5 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 into a graphing calculator or statistical software that can perform exponential regression.

Step2: Calculate exponential regression equation

Using the exponential regression function \(y = ab^{x}\), the calculator will compute the values of \(a\) and \(b\).
For the given data:

• \(a\approx179.693\)
• \(b\approx0.953\)

Answer:

\(y = 179.693\times(0.953)^{x}\)