Rates of change

Rates of change

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  • Yes Bill im fine, i discovered that i have a tumor growing in me
  • Proffeser John what happened to you? are you okay
  • funny you ask, i actually modeled the growth of my tumor and its growth may be represented by the formula f(x)=6^1/4x -0.2
  • Im so sorry to hear that! how big is it?
  • This means that my tumor grows at an exponential rate. The function has a vertical stretch bafo of 6, a vertical compression bafo 4, and a vertical shift 0.2 units down.
  • Okay... Thats interesting i guess... but what exactly does that mean John?
  • haha its painfully funny you ask that Bill
  • Wow! I cannot believe you found all this on your own. By any chance did you find the rates of change?
  • That means that my tumor will average a growth of 5.67 cm per day during that segment! This is known as Average Rate Of Change and is found by using the formula y2-y1/x2-x1
  • Between the fourth day of my tumors existence and the seventh day, the secant through those points will have a linear slope of 5.67
  • What does that mean John?
  • Who cares about average rate of change! I only care about Instantaneous Rate Of Change!
  • Yes yes i found that too. the IROC when x=5 days is 4. this means the slope of the linear tangent at the 5th day is 4!
  • Wow you're a genius!
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