City population A city currently has 36,000 residents and is...

City population A city currently has $36,000$ residents and is adding new residents steadily at the rate of 1600 per year. If the proportion of residents that remain after $t$ years is given by $S(t)=1 /(t+1),$ what is the population of the city seven years from now?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Survival/Retention Functions

A survival or retention function, often represented as S(t), gives the proportion of a population that remains after a certain elapsed time. This function is used to model decay, attrition, or other time?dependent losses in a population, allowing one to determine how many individuals from an initial cohort or from any subsequent cohort continue to remain after t years.

Cohort Analysis

Cohort analysis refers to breaking down the population into groups (cohorts) based on the time they enter the population. Each cohort, such as the initial residents or the residents added in each subsequent year, is subject to the appropriate retention function depending on how long they have been in the population. By analyzing each cohort separately and then summing the surviving members, one can compute the total population at a future time.

Population Growth Modeling

This concept involves understanding how a population changes over time due to factors such as births, deaths, or migration. In problems like the one given, a base population is modified by a constant addition over time, requiring one to account for both the initial number and the incremental changes on an annual basis to determine the future population.

Please give Ace some feedback