1/9 on a calculator is 0.11111111
Initial number of Bacteria = Ao = 100
Number of Bacteria which make the person ill = A = 45,000,000
Growth rate = r = 150% = 1.50
The equation model for this situation is:

Using the values in above equation, we can write:
This means, the person will fall sick after about 14 hours.
Katie won't have more than 100 shells until the 7th day