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**dominicc** *A ‘rogue satellite’ has its distance from Earth, d thousand kilometres, modelled by a cubic function of time, t days after launch. After 1 day it reaches a maximum distance from Earth of 4000 kilometres, then after 2 days it is 2000 kilometres away. It effectively returns to Earth after 3 days, then moves further and further away.*

a What is the satellite’s initial distance from Earth?

b Sketch the graph of d versus t for the first 6 days of travel.

c Express d as a function of t.

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