Worked example: problem involving definite integral (algebraic) | AP Calculus AB | Khan Academy

TL;DR

The population of a town grows at a specific rate, and by using calculus, we can calculate the population growth between two time periods and predict the population at a specific time.

Transcript

• [Instructor] We are told the population of a town grows at a rate of e to the 1.2t power minus two t people per year where t is the number of years. At t equals two years, the town has 1,500 people. First, they ask us approximately by how many people does the population grow between t equals two and t equals five, and then what is the town's popu... Read More

Key Insights

• ☠️ The rate of change of a population can be expressed using calculus and the definite integral of the growth rate equation.
• ⌛ The definite integral represents the accumulation or total change in the population over a specific time period.
• 👻 Calculating the definite integral allows us to determine the population growth and predict the population at a given time.

Summary & Key Takeaways

• The population of a town grows at a rate given by the equation e^(1.2t - 2t), where t represents the number of years.

• To calculate the population growth between two specific times, we need to find the definite integral of the given equation from one time to another.

• By evaluating the definite integral, we can determine that the population of the town grows by approximately 306 people between the second and fifth year, resulting in a population of 1,806 at the fifth year.