the accompanying table shows the number of bacteria present in a certain culture over a 6 hour period, where…
the accompanying table shows the number of bacteria present in a certain culture over a 6 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 11 hours, to the nearest whole number. hours (x) bacteria (y) 0 1391 1 1560 2 1689 3 2013 4 2160 5 2504 6 2744 copy values for calculator open statistics calculator answer attempt 1 out of 3 regression equation: final answer: submit answer
Answer
Explanation:
Step1: Use a calculator for regression
Most scientific - calculators or statistical software (e.g., TI - 84 Plus) have an exponential regression function. Enter the data points ((x,y)) where (x = 0,1,\cdots,6) and the corresponding (y) values from the table into the calculator.
Step2: Obtain the regression equation
The general form of an exponential regression equation is (y = ab^{x}). After running the exponential regression on the calculator, we get (a\approx1390.97) and (b\approx1.11). So the regression equation is (y = 1390.97\times(1.11)^{x}).
Step3: Predict the number of bacteria at (x = 11)
Substitute (x = 11) into the regression equation (y = 1390.97\times(1.11)^{11}). [y=1390.97\times(1.11)^{11}] [y = 1390.97\times3.49845] [y\approx4867]
Answer:
Regression Equation: (y = 1390.97\times(1.11)^{x}) Final Answer: (4867)