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 14 hours, to the nearest whole number.
Hours (x) Bacteria (y)
0 1353
1 1584
2 2037
3 2248
4 2630
5 3146

Answer 1

Explanation:

To find an exponential regression equation for this set of data, we can use a calculator or spreadsheet software with built-in regression functions. Using a calculator, we can input the data points into lists and use the exponential regression function to find the equation:

x y

0 1353

1 1584

2 2037

3 2248

4 2630

5 3146

Using exponential regression, we get the equation y = 1323.119e^(0.216x).

To determine the number of bacteria present after 14 hours, we can plug in x = 14 into the equation:

y = 1323.119e^(0.216 * 14) ≈ 35433

Therefore, the number of bacteria present after 14 hours is approximately 35,433 (rounded to the nearest whole number).