The number of bacteria in a polluted drinking water reservoir was originally 800. In the first hour afterwards, the number of bacteria increased by 320. Assume that the number of bacteria follows a model of logistic growth and that the carrying capacity is 7500.
Let be the number of bacteria after hours. Find , determine the growth model and find how many bacteria there were after and hours.
From the text you see that , , . You find by entering the values into the equation and solving for :
You can now enter straight into the differential equation and solve this to find the growth model:
Solve the differential equation by entering into the formula:
To find the growth model in this case you need to find
. From the text you know the initial condition
. Enter that into the equation for
and you get
This gives the growth model:
You can now find the number of bacteria for and :
The number of bacteria after 5 and 13 hours is and respectively.