Question

3 a colony of bacteria grows exponentially. the table below shows the data collected daily.
state the exponential regression equation for the data, rounding all values to the nearest hundredth.

Explanation:

Step1: Input data into calculator

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

Step2: Calculate exponential regression equation

Using the exponential regression function, the general form of an exponential regression equation is \(y = ab^{x}\). After performing the regression calculation on the data \((0,200),(1,425),(2,570),(3,800),(4,1035),(5,1650),(6,2600)\), we get \(a\approx190.64\) and \(b\approx1.59\)

Answer:

\(y = 190.64(1.59)^{x}\)