Modeling mosquitos with quadratics | Quadratic equations | Algebra I | Khan Academy

TL;DR

The number of mosquitoes in Brooklyn, New York can be modeled by a quadratic function, with the maximum population occurring at 2 centimeters of rainfall.

Transcript

• [Voiceover] The number of mosquitos in millions, M, so M is the number of mosquitos in millions. In Brooklyn, New York it depends on the June rainfall in centimeters, R. So R is the amount of rainfall measured in centimeters. And can be modeled by the function M, so the number of mosquitos in millions, is equal to negative R times R minus four, w... Read More

Key Insights

• 🦟 The mosquito population in Brooklyn, New York is influenced by the amount of rainfall.
• 0️⃣ Zero rainfall or excessive rainfall can result in zero mosquito population.
• 🦟 The maximum mosquito population occurs at 2 centimeters of rainfall.

Questions & Answers

Q: After how many centimeters of rainfall will there be zero million mosquitos?

The model shows that there will be zero mosquitoes at either 0 centimeters or 4 centimeters of rainfall.

Q: What is the maximum possible number of mosquitos?

The maximum number of mosquitoes according to the model is 4 million, which occurs at 2 centimeters of rainfall.

Q: Why does the model imply that excessive rainfall may disrupt mosquito breeding?

Excessive rainfall may lead to water overflow and reduce available standing water, making it difficult for mosquitoes to breed and survive.

Q: What happens to the mosquito population after 4 centimeters of rainfall?

According to the model, the mosquito population starts decreasing after 2 centimeters of rainfall, and at 4 centimeters, it is theoretically negative, although this may not have a practical interpretation.

Summary & Key Takeaways

• The mosquito population (in millions) in Brooklyn, New York is modeled by the function M = -R(R-4), where R is the amount of rainfall in centimeters.

• The model suggests that no rainfall or 4 centimeters of rainfall will result in zero mosquito population, while 2 centimeters of rainfall will lead to the maximum population of 4 million mosquitoes.

• The model implies that some rainfall helps mosquitoes breed, but excessive rainfall may disrupt breeding due to water overflow.