# the differential equation
# y'' +4y=5exp(-x)
f(x)=sin(2*x)+ exp(-x)
TP1=taylor(f(x),x,pi/2,0)
TP2=taylor(f(x),x,pi/2,1)
TP3=taylor(f(x),x,pi/2,1)
TP4=taylor(f(x),x,pi/2,3)
TP5=taylor(f(x),x,pi/2,4)
TP6=taylor(f(x),x,pi/2,5)
p=plot(f(x), -10,50, ymin=-10, ymax=10, gridlines='true')
tp1=plot(TP1, -10,50, ymin=-10, ymax=10, gridlines='true', color='green')
tp2= plot(TP2,-10,50, ymin=-10, ymax=10, gridlines='true', color='red')
tp3= plot(TP3, -10,50, ymin=-10, ymax=10, gridlines='true', color='yellow')
tp4= plot(TP4, -10,50, ymin=-10, ymax=10, gridlines='true', color='purple')
tp5= plot(TP5, -10,50, ymin=-10, ymax=10, gridlines='true', color='orange')
(p+tp1+tp2+tp3+tp4+tp5).show()

a,b=var('a,b')
data=[[1,47.70],[2,25.00],[3,11.35],[4,7.00],[5,4.68],[6,3.02],[7,1.34],[8,0.72],[9,0.49],[10,.31],[11,0.20]]
p1=scatter_plot(data)
p1.show()
model(x)=a*x+b
fit=find_fit(data,model)
print(fit)
a=-3.4976363636461727
b=30.241272727336504
y=a*x+b
p2=plot(y, 0, 15, ymin=0, ymax=50, frame=True, gridlines=True)
print('the line of regression')
show(p1+p2)
print('looking at the graph I would say that the movies gross for the 12th weekend would be 0 or less than that which would mean the movie would lose money')