Final Project

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Final project presentation for AP Calculus BC

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AP Calculus BC: Final Project:

AP Calculus BC: Final Project By: Joseph Lutz

Applications of Calculus in the Real World:

Applications of Calculus in the Real World

Parametric Equations: Projectile Motion:

Parametric Equations: Projectile Motion Usually a topic discussed in Physics, projectile motion is calculated from three things: a quadratic Y-component, a linear X-component, and the force of gravity. The resulting graph created by the parametric equations maps the motion of the projectile, which can then be used for tasks such as gauging the travel distance of a projectile, the effect of gravity on the projectile, often called drop, over time at varying distances.

Source: http://www.ck12.org/book/CK-12-Precalculus-Concepts/section/10.5/:

Source: http://www.ck12.org/book/CK-12-Precalculus-Concepts/section/10.5/ Example 1:

Career: Ballistic Specialist:

Career: Ballistic Specialist Ballistic specialists provide the science behind bullets and the destruction they leave. They can determine the speed, distance, drop, and penetration of any bullet in any situation. Using the projectile motion graph created from parametric equations, and a penetration test, they can determine how a person was shot and from how far and where the shooter shot from. On a constructive note, or destructive, depending on your view, these specialists also design the bullet drop compensation system for scopes on long range rifles, as to make sure a sniper’s bullet hits its mark.

Differentiation: Optimization (Economics):

Differentiation: Optimization (Economics) Differentiation and optimization are found in every facet of life, economics is no exception. Profit and expenses can be given by a differentiable function. The slope of the function, when used to find the critical points of the function, can be used to find the maximum/minimum amount of profit or expense in the financial situation exhibited by the function.

Source: http://tutorial.math.lamar.edu/Classes/CalcI/BusinessApps.aspx:

Source: http://tutorial.math.lamar.edu/Classes/CalcI/BusinessApps.aspx Example 2:

Career: Business Owner:

Career: Business Owner Businesses revolve around optimization, be it profit/expense management or inventory management. For example, my father operates a pressure washing business. As a daily task, he must control and alter the amount of houses he does per week. As the number of contracts increase, the maintenance and material costs increase exponentially. Finding the number of jobs necessary in order to maximize profit while maintaining a steady expense record is vital to the health to his business as well as providing him guidance when buying supplies.

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