Logistics curve

An equation of the form

is called a logistics curve.

In this model growth is rapid at first and then it slows down as y gradually approaches a maximum value.

In this section we will work with

a. ) What is the initial polulation?

Substituting x = 0, we get that = = = 20.

b.) Graph this function. What does y approach as x gets larger and larger?

It appears that y approaches 4000 as x gets larger and larger.

c.) When does y equal 3500?

Solve for x. Multiply both sides by the LCD.

= Thus, This gives us Taking the natural log of both sides give us, Solving this gives us x = 4.826