# 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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