We are given

, defining the

percent of a

population with a given characteristic with

*t* = 0 corresponding to 1960 and

*t* measured in decades.

This

function and its second derivative can be entered into the Y= screen as shown at below.

For this type of function, called a “logistic” model, we know that

and that

is always positive. We set a WINDOW for Y values from 0 to 100 and X values from 0 to 4. The

graph of this

function and the WINDOW are shown below.

It appears that concavity changes from up to down somewhere near *t* = 1.

To see if the second derivative is 0 at a

point near

*t* = 1, we

graph the second derivative which is Y5 in the first screen above. A choice of different values for Y makes the second derivative

graph easier to see.

To find the zero of this second derivative, use

and choose item number 2. You should get about 1

**.**02 which represents the passage of one decade or the beginning of the year 1970 in our problem.