Estou com o seguinte programa para rodar 
	 
	 
 
	N_0 = input('Give initial population size N_0: ') 
	r   = input('Give net growth rate r: ') 
	dt  = input('Give time step size: ') 
	N_t = input('Give number of steps: ') 
	t = np.linspace(0, (int(N_t)+1)*int(dt), int(N_t)+2) 
	N = np.zeros(int(N_t)+2)
 
	N[0] = N_0 
	for n in range(int(N_t)+1): 
	    N[int(n)+1] = N[int(n)] + int(r)*int(dt)*N[int(n)]
 
	import matplotlib.pyplot as plt 
	numerical_sol = 'bo' if int(N_t) < 70 else 'b-' 
	plt.plot(t, N, numerical_sol, t, N_0*np.exp(r*t), 'r-') 
	plt.legend(['numerical', 'exact'], loc='upper left') 
	plt.xlabel('t'); plt.ylabel('N(t)') 
	filestem = 'growth1_%dsteps' % N_t 
	plt.savefig('%s.png' % filestem); plt.savefig('%s.pdf' % filestem) 
	 
	e está dando o seguinte erro: 
	 
	 
 
---> 14 plt.plot(t, N, numerical_sol, t, N_0*np.exp(r*t), 'r-')
     15 plt.legend(['numerical', 'exact'], loc='upper left')
     16 plt.xlabel('t'); plt.ylabel('N(t)')
UFuncTypeError: ufunc 'multiply' did not contain a loop with signature matching types (dtype('<U32'), dtype('<U32')) -> dtype('<U32')
alguém sabe como solucionar