# 8.4 EXPONENTIAL MODEL

(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 ycentral in the interval Δt.

c) Calculate the value of ycum in the interval Δt.

d) Calculate in the interval Δt.

e) Show that the geometric mean of the values of y for t = 3 y t = 6 is equal to ycentral 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.