Your team has observed that over the last several years, the dynamics of the depth of ice in the Columbia Ice Field has on average followed the discrete time dynamical system (DTDS) given by

xt+1=0.9xt+3xt+1=0.9xt+3

where time tt is measured in years, xtxt represents the depth in metres at the beginning of year tt, 0.90.9 represents the fraction of the depth left after summer melt and 33 m is the annual snowfall.

(a) What is the fixed point of this DTDS?

Answer: x=x= __________

FORMATTING: Give an exact answer.

(b) Suppose that in year t=10t=10, you recorded exactly x10=265x10=265 m. What was the depth of the ice field in year 00 of your experiment?

ON PAPER (3 points):

1. WRITE DOWN the general solution formula for the DTDS xt+1=0.9xt+3xt+1=0.9xt+3
2. IDENTIFY what variables are given in the question.
3. SHOW how you use the general solution formula to solve this question.
4. Use at least three decimal places in your intermediate calculations.

Answer (rounded to the nearest integer): x0=x0= ____________ m