Question

2 4 6 Since we now have quadratic and power models that both model curved data, reconsider the previous question. Year PCB Conc. 1 1.0 1.9 a) Notice the power curve in the previous question is not that 4.2 great of a fit to the data (compare the fit of a quadratic 7.2 curve below to the power function above). Use regression 8 11.8 to find a quadratic equation to model the PCB Concentration in Lake Trout data. Round the numbers in your equation to 2 decimal places. b) Use your quadratic equation to estimate the age of a fish with a PCB concentration of 15 ppm, rounded to the nearest tenth 16 14 10 PCB Concentration (ppm) 8 6 4 2 0 0 1 2 3 4 5 6 7 Age

Answer 1

a) The quadratic equation the at best fits the data is shown along with the data points

16 14 12- 10- -8- 9. 2 2 4 8 10 12 14 2

The equation of the curve is

b) We have to solve for x the equation

$15=0.13x^2+0.35 x+0.60 \\ \Rightarrow 0.13x^2+0.35 x-14.40=0 \\ \Rightarrow x={-0.35\sqrt{(0.35)^2-4\times 0.13(-14.40)}\over 2\times 0.13)}\approx -11.96~,~9.26$

Disard the negative value we get

In the 9.3th Year the PCB concentration is 15