#5. If a rancher has one cow with a contagious disease in a herd of 1000, then the time in days “t” for “n” of the cows to become infected is modelled by:
where “ln()” stands for natural logarithm function.
a) Find the number of days that it takes for the disease to spread to 100, 200, 998, and 999 cows.
b) Graph the number of infected cows in the x-axis versus the time in days it takes for infection in the y-axis.
This model, called a logistic growth model, describes how a disease can spread very rapidly at first and then very slowly as nearly all of the population has become infected.