Question

The residents of a certain dormitory have collected the following data: People who live in the dorm can be classified as either involved in a relationship or uninvolved. Among involved people, 15 percent experience a breakup of their relationship every month. Among uninvolved people, 15 percent enter into a relationship every month. What is the steady-state percentage of residents who are uninvolved

Answer 1

the steady-state percentage of residents who are uninvolved is 0.5

Explanation:

Given the data in the question;

let N represent total number of people in the dormitory

I represent people involved in a relationship

and U represent people uninvolved in a relationship.

so

N = I + U

I = N - U ------ let this be equation 1

Rate of Uninvolved = U/N

now, given that rate of break ups B = 15% every month = 0.15

rate of entering into relationship R = 15% every month = 0.15

Now, the steady state condition is;

RU = BI ------- let this be equation 2

such that uninvolved rate is constant.

we input equation 1 into 2;

RU = B( N - U )

we divide both sides by N

RU/N = B( N/N - U/N )

RU/N = B( 1 - U/N )

U/N = B / (B + R)

so we substitute

U/N = 0.15 / (0.15 + 0.15)

U/N = 0.15 / 0.3

U/N = 0.5

Therefore, the steady-state percentage of residents who are uninvolved is 0.5