Question

N=0.04-78.84 Number N of state and federal inmates in millions during year x where x > 2002 can be approximate by the following formula. Determine the year in which there were 1.4 million inmates. It was in the yearwhat year

Answer 1

do you mean
N=0.04x-78.84

Answer 2

the problem is N=0.04-78.84

Answer 3

there should be an x in your formula

Answer 4

I am sorry there is a x

Answer 5

where abouts

Answer 6

year x

Answer 7

\[N(x)=?\]

Answer 8

not sure it says find the year in which there was 1.4 million inmates

Answer 9

But just help me solve it by N(x)=

Answer 10

Is one of these you equation?
\[N(x)=0.04(x)-78.84\]\[\downarrow\]\[N=0.04x-78.84\]

Answer 11

it is the second equation

Answer 12

are ya still there

Answer 13

N is the symbol used in the question for the number of inmates (in millions). If we want to find out in what year we had 1.4 million inmates all we have to do is substitute N=1.4 into the equation and solve to find x. Can you see what to do from here?

Answer 14

no i need help

Answer 15

Ok so can you write out the equation once we substitute N=1.4 in?

Answer 16

do not know for sure

Answer 17

If we substitute N=1.4 we will have as our equation:
1.4=0.04x-78.84
Do you understand how and why I did this?

Answer 18

yes so how do i get the year

Answer 19

Well x is the number of years after 2002 right?

Answer 20

right

Answer 21

So we have to solve the equation:
1.4=0.04x-78.84
to find x. In other words, we have to get x on one side of the equation and everything else on the other side. Do you see what the first step we could take is to do this?

Answer 22

not sure

Answer 23

Well the first thing stopping us from having x on its own on the right hand side of the = is the -78.84. How could we get rid of this?

Answer 24

not sure

Answer 25

Hint: is there something we could add to 0.04x -78.84 to make the right hand side just = 0.04x?

Answer 26

1.4

Answer 27

Not quite, how about this: if we add 78.84 to the right hand side then we will have on the right hand side 0.04x +78.84 - 78.84, which will cancel to give 0.04x. Also, what we do to one side we have to do to the other, so on the left hand side we will have 1.4+78.84. Do you understand?

Answer 28

ok

Answer 29

So after we add 78.84 to both sides of the equation what will we have?

Answer 30

ok so i got 8021 for the left and 78.8 for right

Answer 31

We are adding 78.84 to both sides of the equation:
1.4=0.04x-78.84
So we will have:
1.4+78.84=0.04x-78.84+78.84
Since -78.84+78.84=0, those terms will cancel on the right and we will be left with:
80.24=0.04x
Do you follow my working?

Answer 32

yes so would it be year of 2004

Answer 33

How did you get that? I don't think it's the right answer.

Answer 34

I just throught0.04 meant 2004

Answer 35

No 0.04 means 4/100.
What we want is to get x on its own remember?
So if x is being MULTIPLIED by 0.04, what do you think we have to do to get x on its own?

Answer 36

not sure

Answer 37

What is the opposite to multiplying by something?

Answer 38

dividing

Answer 39

Exactly, so if our x is multiplied by 0.04, then what should we divide by to get x on its own?

Answer 40

I do not know

Answer 41

Let me give a similar example. If 2x=4, then we notice that the x is being multiplied by 2, and so to get x on its own we divide by 2 on both sides to get x=2. Can you apply this method to the question we're doing?

Answer 42

can you help me

Answer 43

I am helping you. We have 80.24=0.04x.
x is being multiplied by 0.04, so to get it on its own we need to divide by 0.04 on BOTH SIDES. Doing this we will get:
80.24 divided by 0.04 = x
So what do you get for x when you put the left hand side into the calculator?

Answer 44

2006

Answer 45

Hooray! Does this answer look sensible, and did you follow the method?

Answer 46

I am going to go back and look it over but thanks for staying with me and helping me this is my first math class.

Answer 47

No worries, if you would like my help in any other questions feel free to ask.

Answer 48

ok thanks