Polynomial identities to describe numerical relationships

Polynomial identities to describe numerical relationships

Positive average rate of change of function example

Positive average rate of change of function example

Geometric series word problem example

Geometric series word problem example

Geometric series for monkey swings

Geometric series for monkey swings

Introduction to factoring higher degree polynomials

Introduction to factoring higher degree polynomials

Cost minimizing choice of inputs

How firms think about tradeoffs between employing more labor or capital.

Hiring for monopsony employer

Labor supply and MPC for a monopsony employer.

Economic profit for a monopoly

Economic profit for a monopoly

Monopolies vs perfect competition

Overview of differences between perfect competition and monopolies.

Economic profit for firms in perfectly competitive markets

Economic profit for firms in perfectly competitive markets

Long run economic profit for perfectly competitive firms

Long run economic profit for perfectly competitive firms

Population growth rate based on birth and death rates

Seeing that the formula for population growth rate based on birth and death rates given in A.P. Biology exams is actually quite intuitive.

Khan Stories: Christian

Ever dream of becoming an astronaut? 👨🏽‍🚀🚀 Eighth grader Christian isn’t just dreaming about it, he’s planting the seeds of his future by growing the same plants as NASA’s International Space Station! 🛰🌱🤩 Do you have a story about Khan Academy you’d like to share? Visit https://www.khanacademy.org/stories. Khan Academy is…

Comparing constants of proportionality

Working example comparing constants of proportionality.

Analyzing related rates problems: equations (Pythagoras)

A crucial part of solving related rates problems is picking an equation that correctly relates the quantities. We recommend making a diagram before doing that.