Question

the accompanying table shows the number of bacteria present in a certain culture over a 5 hour period, where x is the time, in hours, and y is the number of bacteria. write an exponential regression equation for this set of data, rounding all coefficients to the nearest thousandth. using this equation, determine the number of bacteria present after 10 hours, to the nearest whole number.

Explanation:

Step1: Input data into calculator

Input the \(x\) (hours) and \(y\) (bacteria) values into a statistics calculator. The general form of an exponential regression equation is \(y = ab^{x}\).

Step2: Perform exponential regression

Using the calculator's exponential regression function, we find \(a\approx336.000\) and \(b\approx1.350\). So the exponential regression equation is \(y = 336(1.35)^{x}\).

Step3: Calculate for \(x = 10\)

Substitute \(x = 10\) into the equation \(y=336(1.35)^{10}\).
First, calculate \((1.35)^{10}\approx19.2706\).
Then, \(y = 336\times19.2706\approx6475\).

Answer:

The exponential regression equation is \(y = 336(1.35)^{x}\) and the number of bacteria after 10 hours is \(6475\).