(2.4)

Consider a model that relates the characteristic y with time t, through the following basic assumption:

*rir(y)* = -0.4 for 0 < *t* <
∞

Adopt the initial condition: for t = 0, y = 100

1. Write the general expression for the value of the characteristic y at the instant t;

a) Calculate the value of y at the instants

t= 1,2,3,4,5,6.b) Represent, graphically, the values of y calculated above, against the corresponding values of t.

c) Represent, graphically, the values of lny against the given values of t.

2. Considering the interval of time Δt = (3,6)

a) Calculate the variation of y, Δy, during the interval Δt.

b) Calculate y

_{central}in the interval Δt.c) Calculate the value of y

_{cum}in the interval Δt.d) Calculate in the interval Δt.

e) Show that the geometric mean of the values of y for t = 3

yt= 6 is equal to y_{central}and approximately equal to in that interval.f) Show that, in that interval,

3. Consider the interval of time from t = 0 to t = 10. Repeat the calculations of questions 2 item a), c) and d) for this interval.