Answer:
The value of y when t = 4.5 seconds is 130.31.
Step-by-step explanation:
The data provided is:
S = {0, 8.8, 29.9, 62.0, 104.7, 159.1, 222.0, 294.5, 380.4, 471.1, 571.7, 686.8, and 809.2}
Use MATLAB to form the least squares cubic curve equation.
The codes are as follows:
t = [0:1:12]
y = [0,8.8,29.9,62.0,104.7,159.1,222.0,294.5,380.4,471.1,571.7,686.8,809.2];
txt =printf("The coeff of the curve in order of decreasing power are: ");
p = polyfit(t,y,3)
y1 = polyval(p,4.5)
The output is attached below.
The least squares cubic curve equation is:
[tex]y = -0.855769 + 4.702485\cdot t + 5.555370\cdot t^{2}-0.027360\cdot t^{3}[/tex]
The value of y when t = 4.5 is:
[tex]y = -0.855769 + 4.702485\cdot t + 5.555370\cdot t^{2}-0.027360\cdot t^{3}[/tex]
[tex]= -0.855769 + (4.702485\cdot 4.5) + (5.555370\cdot 4.5^{2})-(0.027360\cdot 4.5^{3})\\=130.308476\\\approx 130.31[/tex]
Thus, the value of y when t = 4.5 seconds is 130.31.
