SOLUTION: Can you please help my daughter with some homework. It is very late and this is due tomorrow. Thank you so much. #1 In 1990, the population in a certain town was 45,000 peopl

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Can you please help my daughter with some homework. It is very late and this is due tomorrow. Thank you so much. #1 In 1990, the population in a certain town was 45,000 peopl      Log On


   



Question 409258: Can you please help my daughter with some homework. It is very late and this is due tomorrow. Thank you so much.
#1 In 1990, the population in a certain town was 45,000 people. In 2003 the same town now has 39,750 people.
a) write an equation that models the number of people, P, in terms of the year, t. Let t = 0. Represent 1990.
b) What does the y-intercept represent?
c) What will the population be in 2005?
#2 In 1999, Hasbro made 4.4 million star wars figures for the release of Episode I. In 2002, they made 3.6 million figures for the release of Episode II.
a) write a linear equation that models the number of figures made, y, in terms of the year x. Let x=0 represent 1990.
b) what does the y-intercept represent?
c) How many Star Wars figures would you expect Hasbro to have released in 2005 for the release of Episode III?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
#1
a)
you are given 2 points which are (0,45000) and (3,39750)
2 points are all you need to plot a straight line.
%28P+-+39750%29+%2F+%28t+-+3%29+=+%2845000+-+39750%29+%2F+%280+-+3%29 (point-slope formula)
%28P+-+39750%29+%2F+%28t+-+3%29+=+5250%2F%28-3%29
Multiply both sides by -3%2A%28t+-+3%29
-3%2A%28P+-+39750%29+=+5250%2A%28t+-+3%29
-3P+%2B+119250+=+5250t+-+15750
-3P+=+5250t+-135000
P+=+-1750t+%2B+45000
--------------------
b)
The y-intercept is the population in 1990, at t=0
which is 45,000
c)
Solve for P at t+=+5
P+=+-1750%2A5+%2B+45000
+P+=+36250
---------------------
#2
a)
Here again you have 2 points, (9,4.4) and (12,3.6)
%28y+-+3.6%29%2F%28x+-+12%29+=+%284.4+-+3.6%29+%2F+%289+-+12%29
%28y+-+3.6%29+%2F+%28x+-+12%29+=+.8%2F%28-3%29
%28-3%29%2A%28y+-+3.6%29+=+.8%2A%28x+-+12%29
-3y+%2B+10.8+=+.8x+-+9.6
-3y+=+.8x+-+20.4
+-30y+=+8x+-+204
y+=+%28-4%2F15%29%2Ax+%2B+6.8
-------------------
b)
The y-intercept is millions of figures made in 1990, 6.8 million
c)
y+=+%28-4%2F15%29%2Ax+%2B+6.8
y+=+%28-4%2F15%29%2A15+%2B+6.8
y+=+-4+%2B+6.8
y+=+2.8
2.8 million figures should be released in 2005