Suppose the population of a certain city is 5358 thousand. it is expected to decrease to 4565 thousand in 50 years. find the percent decrease. the percent decrease is approximately nothing%. (round to the nearest tenth.)

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.

its a straight line parallel to the time axis