care4cmodel (version 1.0.3)

exp_decay_rate: Calculate an Exponential Decay Rate From Two Appropriate Pairs of Values

Description

Assuming an exponential decay process y = exp(-r * t), this function calculates r if the following informaion is given:
y_1 = exp(-r \* t_1), y_2 = exp(-r \* t_2)
Hereby, t_1 is the earlier, t_2 the later point in time. This implies the following conditions: t_2 > t_1, y_2 <= y_1
If these conditions are not given, the function will terminate with an error.

Usage

exp_decay_rate(t_1, t_2, y_1, y_2)

Value

The exponential decay rate r, relating to the time unit of t_1 and t_2

Arguments

t_1

Earlier point in time, coupled to y_1

t_2

Later point in time, coupled to y_2

y_1

Earlier value, coupled to t_1

y_2

Later value, coupled to t_2

Examples

  # Up to an age of t_1 = 30, a forest stand of interest has a survival
  # probability of 0.95. Up to an age of t_2 = 80, it has a survival
  # probability of 0.83. If we assume an exponential decay process for the
  # 50-year period, what is the exponential decay rate r?
  r <- exp_decay_rate(30, 80, 0.95, 0.83)
  print(r)

  # Check it
  0.95 * exp(-r * (80 - 30)) # 0.83