Question 3: Real-World Application (20 points)

A population of a species is growing in a habitat, and its growth rate is proportional to both the population and the time.

The differential equation that models this situation is:

dP

dt = kP

Where P is the population at time t, and k is the growth constant. If the initial population is 100, and the population

doubles in 5 years, solve for the population function P(t).

Steps to solve:

• Solve the ODE for P(t).

• Use the initial condition to find the specific solution.

• Interpret the solution in the context of population growth.

asked by guest
on Oct 22, 2024 at 1:25 am



Mathbot Says...

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