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Exponential Regression: Bacteria
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 hundredth. Using this equation, determine the number of bacteria present after 14 hours, to the nearest whole number.
Hours (x) Bacteria (y)
0 629
1 674
2 769
3 934
4 1050
5 1286
Regression Equation:
Final answer:
To find the exponential regression equation for the given data, we can use a scientific calculator or a spreadsheet software. Using Excel, we can create a scatter plot of the data and add a trendline with an exponential model. The resulting equation is:
y = 616.49 * e^(0.1685*x)
Rounding to the nearest hundredth, we get:
y = 616.49 * e^(0.17*x)
To determine the number of bacteria present after 14 hours, we can substitute x = 14 into the equation and evaluate:
y = 616.49 * e^(0.17*14) ≈ 73,452
Rounding to the nearest whole number, we get:
Number of bacteria present after 14 hours ≈ 73,452.
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