# 8.3 SIMPLE LINEAR MODEL

(2.3)

Consider a model that relates the characteristic y with time t, where the basic assumption is:

air(y) = -3, for 0 < t < ∞

Adopt the initial condition: for t = 0, y = 30

1. How would you designate this model?

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

2. Calculate the value of y when t = 0,1,2,3,4,5,6 and draw the graph of y against t.

3. Considering the interval of time, Δt, from t = 2 to t =4

a) Calculate the variation of y during the mentioned interval Δt;

b) Calculate the central value of y in the interval Δt;

c) Calculate the cumulative value of y in that interval, ycum;

d) Calculate the mean value, , of y, in the interval Δt;

e) Calculate the simple arithmetic mean of y in the interval Δt;

f) Verify that the arithmetic mean of y is equal to the mean value, , and equal to the central value, ycentral, of y in that interval.

g) Verify that in the linear model, the amr(y) = air(y) = constant. To do that, calculate, for the above mentioned interval, Δt, the amr(y) and the air(y) and compare the results.

Repeat exercise 3. considering the interval from t = 0 to t = 10.