1.1 Speed and Acceleration in Business - notes

1.1 Speed and Acceleration in Business - notes - Objective...

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Objective [1.1] – Notes Be able to relate the ideas of speed and acceleration to any business relationship (function). One way to get your feet wet with “Calculus” is to think about something we are all very familiar with riding in a car. So…pretend now that you are sitting in your virtual car ready to turn the key. M y first question to you is “Is there a relationship between your position (say your GPS position since you have a new Google Nexus phone) and time? Did you say yes? Ok what generic functional notation can we write? How about …. () p D t Where p is your position and D is the driving relationship and t is time. Rate(speed) Ok, turn the key and I want you to drive off in a “linear” fashion. In other words your d riving (position in time), D, is described by a linear model. Can you describe how you would be driving? Well from pre-calculus you know that a linear relationship has a CONSTANT RATE. Do you know what a constant rate feels like in your car? What you would be doing? Well you would be driving a CONSTANT SPEED maybe with your cruise control. Did you realize that SPEED and RATE describe the same idea? But here is the rub. Say you were driving at 25 miles per hour, a CONSTANT SPEED. Ok but you started out in your driveway at a SPEED of ZERO. So to get to 25 miles per hour you had to change your SPEED(RATE) from zero to 25 miles per hour. Well that is CLEARLY not a CONSTANT RATE(speed) and thus there is NO WAY a linear model could describe you leaving the driveway and getting up to 25mph. Just so you remember ANY model that is not linear is called non-linear. Thus the quadratic, exponential and logistic functions are examples of non- linear models. So follow this.
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1.1 Speed and Acceleration in Business - notes - Objective...

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