Solutions for Jupyter notebook on plotting

Question 1

t= np.linspace(0, 40, 100)
n= 100
lam= 0.34
y= n*np.exp(-lam*t)
plt.figure()
plt.plot(t, y)
plt.yscale('log')
plt.show()

Question 2

x= np.linspace(0, 10, 200)
plt.figure()
plt.plot(x, np.sin(x), label= 'sin(x)')
plt.plot(x, np.sin(2*x), label= 'sin(2x)')
plt.legend()
plt.title('sin(x) and sin(2x)')
plt.xlabel('x')
plt.show()

Question 3

sig= 2
m= 0.1
x= np.linspace(-8, 8, 500)
y= np.exp(-(x - m)**2/2/sig**2)/np.sqrt(2*np.pi)/sig
plt.figure()
plt.plot(x, y)
plt.fill_between(x, np.zeros(x.shape), y, alpha= 0.5)
plt.ylim(bottom= 0)
plt.show()

Question 4

KT= 1
KR= KT/50
L= 0.9
x= np.linspace(0, 100, 1000)
plt.subplot(2,1,1)
plt.plot(x, (1 + KT*x)/((1 + KT*x) + L*(1 + KR*x)), label= 'n= 1')
plt.plot(x, (1 + KT*x)**2/((1 + KT*x)**2 + L*(1 + KR*x)**2), label= 'n= 2')
plt.xscale('log')
plt.ylabel('fraction activated')
plt.legend()
plt.subplot(2,1,2)
plt.plot(x, (1 + KT*x)**4/((1 + KT*x)**4 + L*(1 + KR*x)**4), label= 'n= 4')
plt.plot(x, (1 + KT*x)**8/((1 + KT*x)**8 + L*(1 + KR*x)**8), label= 'n= 8')
plt.xscale('log')
plt.ylabel('fraction activated')
plt.xlabel('[X]')
plt.legend()
plt.tight_layout()