Nonlinear Project

Nonlinear Project

Quadratic Model

(QR-1)

(QR-2) The formula for the quadratic polynomial is: y = -0.3476x2 + 10.948x – 23.078

(QR-3) The coefficient of determination is: r2 = 0.9699

The closer r2 is to 1, the better the relationship; with an r2 of 0.9699 which is close to 1

there is a strong relationship or good fit. A parabola is a good fit for the data.

(QR-4) According to the model, at 13:19 the temperature will be around 61. Take 13:19 and

Convert it to 13.31667 then put it in the formula for x. The answer is 61.07 degrees.

Y = -0.3476 (13.31667)2 + 10.948 (13.31667) – 23.078 = 61.07

(QR-5) X = -b ± √(b2-4ac) = -b ± √(b2-4ac)

2a 2a 2a

So the highest temperature will be at –b = -10.948 = 15.74799

2a 2(-.3476)

Which is approximately 15.75, or 15:45

The temperature is -0.3476(15.75)2 + 10.948(15.75) – 23.078 = 63.12648

So the highest temperature of the day is 63.1 degrees at 15:45

(QR-6) 61 = -0.3476x2 + 10.948x -23.078

0 = -0.3476x2 + 10.948x -84.078

-10.948 ± √(10.9482 - 4(-.3476)(-84.078) = 13.27 and 18.22

2(-.3476)

The times of day in which the temperature is 61 degrees will be around 13:15 and

18:15

Exponential Model

(ER-1)

(ER-2) The formula for the exponential function of best fit is: y = 89.976e-0.023x

(ER-3) The coefficient of determination is: r2 = 0.9848. Because the coefficient of determination is close to 1 there is a strong fit. The exponential curve is a good fit to this data.

(ER-4) y = 89.976e(-0.023)(21) = 55.509 T = y + 69 = 55.509 + 69 = 124.509

After 21...