A Gompertz curve is the graph of a function of the general form N(t) = CA^Bt where A, B, and C are constants. Such curves are used by psychologists and others to describe such things as learning and growth within an organization.^†

a. Suppose the personnel director of a large corporation determines that after t years, the corporation will have N(t) = 500(0.03)^(0.4)t employees. How many employees are there originally (at time t = 0)? How many are there after 5 years? When will there be 300 employees? How many employees will there be in the long run?

b. Sketch the graph of N(t). Then, on the same graph sketch the graph of the Gompertz function

How would you describe the relationship between the two graphs?

Transcribed Image Text:

F(t) = 500(0.03)-(0.4)-¹