Exponential Growth and Decay Calculus, Relative Growth Rate, Differential Equations, Word Problems

TL;DR

This video discusses the concept of exponential growth and decay in population growth, explaining how to calculate population at any given time and determine the relative growth rate.

Transcript

in this video we're going to talk about exponential growth and decay problems as it relates to population growth so to speak now the first equation you need to be familiar with is this equation dp divided by dt is equal to k times p so this equation tells us that the population grows at a rate that is proportional to the size of the population the ... Read More

Key Insights

• ☠️ The equation dp/dt = k * p represents the rate of population growth, where k is the relative growth rate and p is the population size.
• ⌛ By integrating the equation and using logarithmic functions, a general formula p(t) = p₀ * e^(k * t) is derived to calculate the population at any given time.
• ☠️ The relative growth rate (k) can be determined using data points and the general formula.

Summary & Key Takeaways

• The equation dp/dt = k * p represents the rate at which a population grows, where dp/dt is the population growth rate, k is the relative growth rate, and p is the population size.

• By integrating the equation and applying logarithmic functions, a general formula is derived to calculate the population at any given time.

• Using a specific example, the video demonstrates how to calculate the relative growth rate and use the general formula to determine the population at different time points.