friendzone
  • friendzone
Membership of Gym Day # of Members 1 2 2 4 3 8 4 16 Question: Philip started a new gym and kept track of the total number of members that he had. The data for the first four days is shown in the table. A. Create a scatterplot of the number of members. B. Should this pattern be modeled by a linear function? Explain. C. By the end of the first week Philip would like to have 125 members. Will he reach his goal? Show your work.
Mathematics
jamiebookeater
  • jamiebookeater
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friendzone
  • friendzone
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johnweldon1993
  • johnweldon1993
So scatterplot would just be putting the points.. |dw:1433594869797:dw| Now we can see (kinda from my drawing) that we do not have a straight line connecting all these points...this is where part B comes in...as this is NOT a linear model
sohailiftikhar
  • sohailiftikhar
after one week it should 128 members according to the sequence given in the data ...

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johnweldon1993
  • johnweldon1993
And we can explain that by stating in order for this to be a linear model..all of the slopes between points must be constant.... Between points 1 and 2 the slope is \(\large \frac{4 - 2}{2-1} = 2\) and the slope between points 2 and 3 is \(\large \frac{8-4}{3-2} = 4\) so since the slope is not consistent...this is not a linear model
sohailiftikhar
  • sohailiftikhar
it is not a linear relation between the days and members its quadratic relation...
johnweldon1993
  • johnweldon1993
Now as far as part C goes...we can see that as 'x' goes up by 1....'y' goes up by 2 times the previous 'y' value We can write this as an expression \(\large y = 2^x\) *when we plug in x = 1...we get 2 when we plug in x=2 we get 4 x = 3, y = 8 just like above So we can see this is actually an exponential function So in order to see how many members we have after the first week *meaning 7 days* we just plug in x = 7 there \(\large y = 2^7 = 128\) members so yes he will have enough
sohailiftikhar
  • sohailiftikhar
its a simple Question dude do not make it so complicated ....
johnweldon1993
  • johnweldon1993
It's called actually explaining it rather than giving the answers bro
sohailiftikhar
  • sohailiftikhar
nice work ...

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