Answer :
Using the differential equation, the population after 30 years is 760.44.
What is meant by differential equation?
- In mathematics, a differential equation is a relationship between the derivatives of one or more unknown functions.
- Applications frequently involve a function that represents a physical quantity, derivatives that show the rates at a differential equation that forms a relationship between the three, and a function that represents how those values change.
- A differential equation is one that has one or more functions and their derivatives.
- The derivatives of a function define how quickly it changes at a given location.
- It is frequently used in disciplines including physics, engineering, biology, and others.
The population P after t years obeys the differential equation:
- dP / dt = kP
Where P(0) = 500 is the initial condition and k is a positive constant.
- ∫ 1/P dP = ∫ kdt
- ln |P| = kt + C
- |P| = e^ce^kt
Using P(0) = 500 gives 500 = Ae⁰.
- A = 500.
- Thus, P = 500e^kt
Furthermore,
- P(10) = 500 × 115% = 575sO
- 575 = 500e^10k
- e^10k = 1.15
- 10 k = ln (1.15)
- k = In(1.15)/10 ≈ 0.0140
- Therefore, P = 500e^0.014t.
The population after 30 years is:
- P = 500e^0.014(30) = 760.44
Therefore, using the differential equation, the population after 30 years is 760.44.
To learn more about differential equations refer to:
brainly.com/question/1164377
#SPJ4
