Question

A private school opened in 2005 with an initial enrollment of 85 students. The enrollment has increased by an average of 18 students each year since the school opened. A nearby public school had an enrollment of 95 in 2005, and its enrollment has increased by an average of 15 students per year.

Let t = time in years, with t = 0 representing the year 2005. Let f(t) = the number of students enrolled at the private school and g(t) = the number of students enrolled at the public school. Create the two functions to represent the situation.
Graph the system of equations to determine the the point of intersection.
Interpret the point of intersection in the context of the problem.

Answer 1

http://flockdraw.com/8cq4mv

Answer 2

What is with the link?

Answer 3

its so i we can work it out together

Answer 4

Do you know how to draw a line?

Answer 5

? yes i dont how to do this prblem

Answer 6

First think is you want to list out the value of each function for different values of \(t\).

Answer 7

? ><ok

Answer 8

"2005 with an initial enrollment of 85 students. The enrollment has increased by an average of 18 students each year since the school opened"

Answer 9

"2005 with an initial enrollment of 85 students"

We'll say that \(t=0\) at 2005 since that is where we start to keep track.

Answer 10

Our function will look like: \[
f(t) = mt+b
\]where \(m\) is slope and \(b\) is \(y\) intercept.

Do you follow?

Answer 11

kinda

Answer 12

This is the equation of a line.

Answer 13

The slope intercept form.

Answer 14

mhh o.o

Answer 15

They never taught you about slope intercept form?

Answer 16

y=mx+b?

Answer 17

Yes, but this time the input variable is \(t\) not \(x\).
And the output is \(f(t)\) not \(y\)

Answer 18

Other than that, everything is the same.

Answer 19

initial enrollment of 85
This means \(b=85\)
increased by an average of 18
This means \(m=18\)

Answer 20

mhh o.o i c

Answer 21

So the first equation is \[
f(t)=18t+85
\]

Answer 22

Can you do the same thing for:
" A nearby public school had an enrollment of 95 in 2005, and its enrollment has increased by an average of 15 students per year."

Answer 23

yes o.o

Answer 24

Okay let's see what you get.

Answer 25

f(t)=mt+b f(t)=15t +95?

Answer 26

". Let f(t) = the number of students enrolled at the private school and g(t) = the number of students enrolled at the public school."

So this time we want to use \(g(t)\) not \(f(t)\)

Answer 27

so its still the same ? but juss with a g?

Answer 28

Yeah.

Answer 29

g(t)=15t +95 i c ! : )

Answer 30

Now you want to see what happen when \(t=0,1,2,3\)

Answer 31

That will give you some points.

Answer 32

can we do it on the website ? i also need to show the graph >~<

Answer 33

ok plot the points.

Answer 34

so i substitute for t =0,1,2,3,

Answer 35

does the website still work ?

Answer 36

Yes, then you can plot the points.

Answer 37

yeah

Answer 38

okay : ) so f(0)=18(0)+85

Answer 39

how would or wat do i need to do now?

Answer 40

f=0+85

Answer 41

\[f(0) = 18(0)+85=0+85=85\]

Answer 42

So one point is \((0,85)\)

Answer 43

http://flockdraw.com/8ztk5e

Answer 44

do i need a legend or key?

Answer 45

ON the bottom you should put like 0,1,2,3...
On the side you should put maybe 80,90,100,110

Answer 46

ookay i did that

Answer 47

so f(1)=18(1)+85 --> f=18+85
f= 100 but i plot it as 18, 85?

Answer 48

The point would be \((1,100)\)

Answer 49

Each point is \((t,f(t))\)

Answer 50

O-O ohh so.. if i do f(3)=18(3)+85 --> F=54+85
F=139 . so it would be (1,139)?

Answer 51

ohh (3,139)?

Answer 52

Yes.

Answer 53

Now you can find points for \(g(t)\)

Answer 54

yes ! : ) so i do the same right ? to the g(t)

Answer 55

Yep

Answer 56

students is y and /top
x is years ? bottom

Answer 57

so for F ive got
0,85
1.103
2,121
3,139
G
0,95
1,110
2,125
3,140

Answer 58

Okay, good. Now you need to plot those points on a graph and you're done.

Answer 59

do i plot G like i do to F?

Answer 60

Yes, plot them on the same graph.

Answer 61

You might also want to plot \(t=4\) as well.

Answer 62

wat u mean plot t=4?

Answer 63

Meaning plot \((4,f(4))\) and \((4,g(4))\)

Answer 64

4,4 for both G and F?

Answer 65

No, what is \(f(4)\)?

Answer 66

f(4)=18(4)+85?

Answer 67

Yes

Answer 68

oh ! : ) okay = (4,157

Answer 69

Now do that for g(t) and we'll have enough points.

Answer 70

4,155

Answer 71

Yeah, just plot all the points and you'll get it.

Answer 72

http://flockdraw.com/8ztk5e

Answer 73

Now use line tool

Answer 74

http://www.wolframalpha.com/input/?i=f(t)%3D18t%2B85%2C+g(t)%3D15t+%2B95

Answer 75

?

Answer 76

That shows you what the lines would look like.

Answer 77

i tho i plot 0,85 1.103 2,121 3,139 & 0,95 1,110 2,125 3,140 ?

Answer 78

Yeah

Answer 79

interception is ? 4 ?

Answer 80

@wio ? ><

Answer 81

It is near 4