Write a differential equation that express the law of natural growth.
Solution: If dydx=ky, then y=cekt.
Given: The law of natural growth.
If dydx=ky, then y=cekt.
Where c is the initial amount present.
K is either a growth or decay constant.
K is positive: equation represents growth.
K is negative: equation represents decay.
Conclusion: Hence, if dydx=ky then y=cekt for law of natural growth.
To determine: Under what circumstances is this an appropriate model of population growth.
Solution: Exponential growth, biotic potential, environmental resistance.
Given: Appropriate model of population growth.
The circumstances is given below:
Exponential growth: - Number of individuals added each generation increases as the total number of family increases.
Biotic potential: - Biotic potential is maximum population growth that can possibly occurs under ideal circumstances.
Environmental resistance: - Environmental resistance is all environmental condition that prevent population from achieving biotic potential.
Conclusion: Hence, exponential growth, biotic potential and environmental resistance are under circumstance.
To determine: What are the solution of the equation, dydx=ky, y=cekt.
Given: dydx=ky and y=cekt.
Conclusion: Hence, the solution is kcekt.