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Question 485419: I have 3 questions that needs to be answered using a graph, but I am unable to copy and paste alone with the questions. I will explain the graph. Here are the instructions and questions:
The following graph shows data regarding the population of Rochester, New York. Original projections predicted the same population in half the number of years.
Answer the following questions. Please show all of your work.
At what rate was the population changing?
At what rate did the projections predict the population would change?
What was the predicted population in 2003?
the graph shows the population started at 350,000; declined to 300,000 in 2 years. Then decline again to 250,000 in 4 years.
Thank you for your help.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i'll work in thousands.
you start at 350 thousand in year 0, drop to 300 thousand in year 2 and drop to 250 thousand in year 4.
you are dropping 50 thousand every 2 years or 25000 a year.
your equation is y = -25x + 350
your graph looks like this.
the horizontal lines are at y = 350, 300, and 250 thousand.
when x = 0, y = 350 thousand
when x = 2, y = 300 thousand
when x = 4, y = 250 thousand
the problem statement says:
original projections predicated the same population in half the number of years.
this means that Rochester was projected to have 300 thousand in 1 year and 250 thousand in 2 years.
that would be a drop in population of 50 thousand per year.
the equation for that would be y = -50x + 350
add that equation to the graph and it looks like what you see below.
you can see that the first equation crosses the 300 thousand line in 2 years and the 250 thousand line in 4 years, while the second equation crosses the 300 thousand line in 1 year and the 250 thousand line in 2 years.
answers to your questions are below:
At what rate was the population changing?
it changed at the rate of minus 25 thousand per year.
At what rate did the projections predict the population would change?
the projections predicted the population would change at the rate of minus 50 thousand per year.
What was the predicted population in 2003?
it depends on when you started.
the predicted population decreased by 50 thousand per year.
it started at 350 thousand.
if the start year is 2000, then 2003 is 3 years from that and the predicted population would be 350 thousand minus 3*50 thousand = 350 thousand minus 150 thousand = 200 thousand.
find the start year and subtract it from 2003. multiply 50 thousand by the number of years and subtract it from 350 thousand.
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