Math Please Solve this question

Algebra
Tutor: None Selected Time limit: 1 Day

Oct 14th, 2014

a) You have to find a linear function that fits the data, namely that equal 291 when x = 5 (because in 2005, 5 years after 2000 contributions was 291 mln.) and equal 396.1 when x = 7 (because in 2007, 7 years after 2000 contributions was 396.1 mln.).

Linear function always looks like y = a*x + b. Our goal now is to find parameters "a" an "b".

We know that when x = 5, y = 291. We should put it in our function. That gives us equation :

291 = a*5 + b.  (1)

Similarly we can get an equation from the information that when x = 7, y = 396.1 :

396.1 = a*7 + b.  (2)

Now we can subtract equation (1) from equation (2), by subtracting both sides of equations:

396.1 - 291 = a*7+b - (a*5 + b) = a*7+b - a*5 - b.

Now we can simplify both sides :

105.1 = a*2.

And devide it on 2 to get parameter "a" :

a = 105.1 / 2 = 52.55.

Then we can put it into equation (1) to get the value of "b" :

291 =a*5 + b = (52.55)*5 + b = 262.75 + b.

Hence

b = 291 - 265.75 = 28.25

By putting this parameters into general linear equation y = a*x + b we get an answer:

y = 52.55 * x + 28.25

b) You have to use that function for prediction of contribution in 2010.

Namely you have to find "y", when x = 10 (2010 is 10 years later 2000) :

y = 52.55*x + 28.25 = 525.5 + 28.25 = 553.75.

And that is your answer (in millions) : 

y = 553.75


Oct 14th, 2014

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