Biology: Some types of worms have a remarkable ability to live without moisture. The following table from one study shows the number of worms W surviving after x days without moisture.x (days) 0 20 40 80 120 160

W (worms) 50 48 45 36 20 3(a) Use the equation W= -0.0014x^2 – 0.076x + 50 to find W for each x-value in the table.(b) Discuss how well this equation approximates the data. (c) Use this equation to estimate the number of worms on day 60 and on day 180. Which answer is most accurate? Explain.(a) Using the equation W= -0.0014x^2 – 0.076x + 50, we obtain the following values for Wx (days) 0 20 40 80 120 160

W (worms) 50 47.92 44.72 34.96 20.72 2So if we round W to the nearest integer, we getx (days) 0 20 40 80 120 160

W (worms) 50 48 45 35 21 2(b) The equation approximates the data very well. The values of W agree with our original data with the error of no more than one unit.(c) For x=60, W=-0.0014(60)^2 – 0.076(60) + 50 = 40.4 or about 40 worms.

So the model predicts that there will be 40 worms on day 60. This answer is most accurate since x=40 lies inside the original interval from 0 to 160. For x=180, W= -0.0014(180)^2 – 0.076(180) + 50 = -9.04We see that this negative answer does not even make sense in the context of our problem. In fact, when x=163, W=0.4154 or about 0 worms. Since the parabola continues beyond this point, the negative values of W no longer make sense since there will be no more worms left after 163 days. In general, we have to be careful with extrapolated values of W since the model is based on values that lie inside the interval from 0 to 160. The model may fail to be accurate for values outside this interval.

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