ExponentialChange

Exponential growth or decline of connected stock

Diagram

Information

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ExponentialChange will fill (or drain) the connected stock from a source (or into a sink) with infinite capacity at a rate that is determined at any time as the product of the current amount in the connected stock and the fractional rate given by the real input u. By convention, a positive rate will fill the stock, while a negative rate will drain it.

Notes

  • By default it is assumed, that the rate given is a continously compounding rate (isCCR = true). If this is not case, the rate will be converted using the →ForceOfInterest converter.

  • Care has to be taken in case an →InformationLevel with a negative level is connected to the ExponentialChange, as the sign of the effective rate is affected by this.
  • Exponential change processes have a constant doubling time (or a constant half-life) which can be found by dividing log(2) ≈ 0.69 by the continuously compounding fractional rate (or by log(1+rate) if the rate is not a continuously compounding rate).

See also

ExponentialGrowthExponentialDecline, ExponentialDecay

Parameters (1)

isCCR

Value: true

Type: Boolean

Description: = true, if the factional rate given is assumed to be a continuously compounding rate else the rate will be converted

Inputs (1)

u

Type: RealInput

Description: Input signal

Connectors (5)

y

Type: RealOutput

Description: Rate information

y1

Type: RealOutput

Description: Rate information

y2

Type: RealOutput

Description: Rate information

massPort

Type: FlowPort

Description: Inflow to or outflow from connected stock

u

Type: RealInput

Description: Input signal

Components (6)

cloud

Type: Cloud

Description: Reservoir (stock/level) with an infinite capacity

changing

Type: Switching

Description: An exchange of matter between two stocks at an exogenous rate

stockLevel

Type: FlowPortSensor

Description: LEvel of connected stock

changingRate

Type: Product_2

Description: Inputs are multiplied

indicatedFractionalRate

Type: PassThrough

Description: Output is equal to input

ccRate

Type: ForceOfInterest

Description: Continuously Compounding Rate

Used in Components (3)

ExponentialChange

BusinessSimulation.CausalLoop

Exponential growth or decline process

Elasticity

BusinessSimulation.CausalLoop

Fractional rate of change is proportional to that of the influencing stock

LinearInteraction

BusinessSimulation.Flows.Interaction

Linear model of interaction between two stocks