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

Use a graphing calculator or statistical software. Input the \(x\) - values (days: \(0,1,2,3,4,5,6\)) and \(y\) - values (populations: \(200,425,570,800,1035,1650,2600\)).

Step2: Perform exponential regression

On a TI - 84 Plus (for example), go to STAT > CALC > ExpReg. The general form of an exponential regression equation is \(y = ab^{x}\).
The calculator will output values for \(a\) and \(b\).
When we perform the exponential regression on the given data:
The value of \(a\approx199.94\) and \(b\approx1.59\)

Answer:

\(y = 199.94(1.59)^{x}\)