Question

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.

Answer 1

Draw your answer below:

Answer 2

So scatterplot would just be putting the points..



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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

nice work ...