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## anonymous one year ago 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.

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1. anonymous

Draw your answer below:

2. 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

3. anonymous

after one week it should 128 members according to the sequence given in the data ...

4. 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

5. anonymous

it is not a linear relation between the days and members its quadratic relation...

6. 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

7. anonymous

its a simple Question dude do not make it so complicated ....

8. johnweldon1993

It's called actually explaining it rather than giving the answers bro

9. anonymous

nice work ...

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