How can I code the logistic growth?

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Python

I have to code the logistic growth in python where time can take float numbers.

dN/dt = rN(1-N/K)
where
N is the population
r is the growth rate
K is the carrying capacity
t is the time


The time in my code can take only integers but it must definitely take float numbers as later I will use it for the logistic growth of the tumours and I couldn't fix it.

I will really appreciate all the help possible even if it is not related to my code.

What I have tried:

import numpy as np #for basic numerical computation
import matplotlib.pyplot as plt #for visualization
import csv
import random
#val = int(input("Enter your value: ")) 
r = .25 # growth rate / year ,|(birth/death rate)
K = 100 # carrying capacity
#t = 40 # time
t=random.randint(0,40)
num = np.zeros(t+1)#always add +1 for your upper limit #array([ 0.,  0.,  0.,  0.,  0.]) which means that it creates 41 arrays filled with zeroes 
num[0] = 1
for i in range(t):
    num[i+1] = num[i]+r*num[i]*(1-num[i]/K)
    row= (i+1,'\t\t',format(num[i], '.8f'))
    print (row)
    with open('plot.csv', 'a') as csvFile:
            writer = csv.writer(csvFile, delimiter=' ')
            writer.writerow(row)
            csvFile.close()
plt.plot(range(t+1),num, 'b')
plt.xlabel('Time')
plt.ylabel(' Cell Number')
plt.title('Logistic Growth')
plt.axvline(np.argmax(np.diff(num)),  color = 'k'  )
plt.show()