{"id":10608,"date":"2017-07-05T16:53:24","date_gmt":"2017-07-05T23:53:24","guid":{"rendered":"https:\/\/magoosh.com\/hs\/?p=10608"},"modified":"2017-07-02T16:54:40","modified_gmt":"2017-07-02T23:54:40","slug":"ap-calculus-logistics-growth-model","status":"publish","type":"post","link":"https:\/\/magoosh.com\/hs\/ap\/ap-calculus-logistics-growth-model\/","title":{"rendered":"AP Calculus BC Review: Logistics Growth Model"},"content":{"rendered":"

What is the logistics growth model, and how does it work in problems on the AP Calculus BC exam? This review article will explain what you need to know for the test.<\/p>\n

\"taking<\/p>\n

The Logistics Growth Model<\/h2>\n

The logistics growth model<\/strong> is a certain differential equation<\/strong> that describes how a quantity might grow quickly at first and then level off.<\/p>\n

Let y<\/em> stand for the quantity, which is often population. In the logistics model, the rate of change of y<\/em> is proportional<\/em> to both the amount present and the different between the amount and a fixed carrying capacity, M<\/em>.<\/strong><\/p>\n

In mathematical language, we would say there is a positive constant k<\/em> such that:<\/p>\n

\"Logistics<\/p>\n

The following equivalent form of the equation is also useful (though the constant k<\/em> may have a different value).<\/p>\n

\"Logistics<\/p>\n

Interpreting the Model<\/h3>\n

Most often on the AP Calculus BC exam, your job will be to interpret the model. You should be able to find out characteristics of the model without explicitly solving for y<\/em>.<\/p>\n

Based on the form of the differential equation, we can find the general shape of the logistics model. The resulting graph is the logistics curve<\/strong>.<\/p>\n

\"Logistics<\/p>\n

There are a few important things to note.<\/p>\n