Answer:
The population decreases at the rate of 0.32% a year.
Step-by-step explanation:
The population of this certain city can be modeled by this following differential equation.
where r is the growth rate(r>0 means that the population increases, r < 0 it decreases).
We can solve this by the variable separation method. We have that:
Integrating both sides, we have
where P(0) is the initial population.
To find P in function of t, we apply the exponential to both sides.
The initial population of the city 5,358,000. So P(0) = 5,358,000.
It decreases to 4,565,000 in 50 years. So P(50) = 4,565,000.
Applying to the bold equation:
To find the growth rate, we apply ln to both sides.
r =
The population decreases at the rate of 0.32% a year.