SOLUTION: This is a story problem and i have to find two equations. one is linear and one is quadratic. here is the problem: "Two very lucky twin brothers have very wealthy parents wh

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Question 186794: This is a story problem and i have to find two equations.
one is linear and one is quadratic.
here is the problem:
"Two very lucky twin brothers have very wealthy parents who offered them very generous allowances at the tender age of 8 years old. the boys had 2 choices. under Option 1, they could take a monthly allowance of $100 this year (year 0) and expect a $100 raise every year until they turn 18 (year 10). Under option 2 they could take a monthly allowance of $5 this year (year 0), and the amount would double every year until they turn 18 (year 10). What are the equations that would represent each option?"
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
This is a story problem and i have to find two equations.
one is linear and one is quadratic.
here is the problem:
"Two very lucky twin brothers have very wealthy parents who offered them very generous allowances at the tender age of 8 years old. the boys had 2 choices. under Option 1, they could take a monthly allowance of $100 this year (year 0) and expect a $100 raise every year until they turn 18 (year 10). Under option 2 they could take a monthly allowance of $5 this year (year 0), and the amount would double every year until they turn 18 (year 10). What are the equations that would represent each option?"

The first, option 1, is indeed a linear equation.

A linear equation has a graph which is a straight line. A straight line
is determined by two points.

for the year 1, their allowance is $100
for the year 2, their allowance is $200

Let x = the year number and y = the allowance.

So the line which the graph of the equation goes through
the two points (1,100), and (2,200)

First we find the slope, given by the slope formula 

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

m=%28200-100%29%2F%282-1%29

m=100%2F1

m=100

Now we substitute in the point-slope formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29
y-100=100%28x-1%29
y-100=100x-100
y=100x

So the 9th year their allowance will be found by
substituting x=9, giving an allowance of y=$900.

I can't tell from the wording whether they get an allowance
the 10th year or not, for it says "until they are 18".  Literally
that means the last year they get an allowance is the 9th year.
You'll have to ask your teacher whether they get an allowance on the
10th year or not.  If so it will be $1000.

----------------------

However option 2 is NOT a quadratic equation.  It is a geometric
sequence.  The formula for the nth term of a geometric series is

a%5Bn%5D=a%5B1%5Dr%5E%28n-1%29

where the nth term is a%5Bn%5D, a%5B1%5D=5 and r=2,
since it doubles every year.  Substituting these:

For the 9th year, the allowance will be

a%5Bn%5D=a%5B1%5Dr%5E%28n-1%29
a%5B9%5D=5%2A2%5E%289-1%29
a%5B9%5D=5%2A2%5E8
a%5B9%5D=5%2A256
a%5B9%5D=1280

So the 9th year the allowance will be $1280.
The 10th year it will be

a%5Bn%5D=a%5B1%5Dr%5E%28n-1%29
a%5B9%5D=5%2A2%5E%2810-1%29
a%5B9%5D=5%2A2%5E9
a%5B9%5D=5%2A512
a%5B9%5D=2560

So the 10th year the allowance would be $2560.
-------------------
Comment:
Maybe the first one was supposed to be done as
an arithmetic series, which would give you the same
answer as the linear way.  If so post again.  
But option 2 is definitely a geometric sequence
and is not a quadratic.  

Edwin