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.
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