dtds

Question 1

A DTDS consists of…

Answer 1

1. a quantity whose change is tracked at time t
2. a time step (ex: days, years - the unit in which t is measured)
3. an updating function f that describes the change during a single time step [x_t+t = f(x_t)]

Question 2

The updating function describes…

Answer 2

… the CHANGE from one time step to another - NOT the measured value at time T (ie we calculate f(x_t), not f(t) ).

Question 3

solution to a DTDS

Answer 3

Question 4

linear dtds updating function

Answer 4

x_t+1 = f(x_t) = rx_t + c

where r = rate and c = constant added each time

Question 5

general fixed point solution

Answer 5

fixed point = a point that satisifies the equation

f(x_t) = (x_t)

Question 6

linear dtds fixed point formula

Answer 6

x* = d / (1-r)

where d = amount (constant) added each time and r = rate

Question 7

linear dtds general solution

Answer 7

Question 8

cobwebbing algorithm

Answer 8

Question 9

stability of a fixed point

Answer 9

Question 10

Newton’s method

Answer 10