Question 1037042: In 2005, it took 21.43 currency units to equal the value of 1 currency unit in 1914. In 1990, it took only 14.20 currency units to equal the value of 1 currency unit in 1914. The amount it takes to equal the value of 1 currency unit in 1914 can be estimated by the linear function V given by V(x)=0.4967x-14.8414, where x is the number of years since 1990.Thus, V(11) gives the amount it took in 2001 to equal the value of 1 currency unit in 1914. Use this function to predict the amount it will take in 2008 and in 2017 to equal the value of 1 currency unit in 1914.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the formula you are given is v(x) = .4967*x - 14.8414, where x is the number of years since 1990.
i believe you meant v(x) = .4967*x + 14.8414.
otherwise the formula doesn't make any sense.
let's take a look at what the formula would tell you for the following years.
in 1990, x = 1990 - 1990 = 0.
the formula becomes v(0) = .4967*0 + 14.8414 = 14.8414.
since that's pretty close to the actual of 14.20, it makes sense.
in 2005, x = 2005 - 1990 = 15.
the formula becomes v(15) = .4967*15 + 14.8414 = 22.292.
since that's pretty close to the actual of 21.43, it makes sense.
you do not expect the formula to give you an estimate that's right on, since the formula is a straight line formula that's derived from data that is not straight line in nature.
so, using this formula with the change that i made, you can use it to estimate 2008 and 2017.
in 2008, x = 2008 - 1990 = 18.
the formula becomes v(18) = .4967*18 + 14.8414 = 23.782.
in 2017, x = 2017 - 1990 = 27.
the formula becomes v(27) = .4967*27 + 14.8414 = 28.252.
you can graph this formula and you should be able to see the data points.
the formula to graph is y = .4967 + .8414
it looks like this:
you can see the data points on the grpah.
i also looked up an inflation calculator to see if the formula makes sense.
it appears to be reasonably close to the figures from this formula.
once again, the numbers won't be right on because the inflation growth rate is not linear, but close enough to linear that it can be modeled with a straight line equation.
here's the link to the inflation calculator that i found.
http://www.usinflationcalculator.com/
using this calculator, you would estimate 2005 as follows:
enter 1914 for if in year.
enter 1 for purchased an amount for.
enter the year you are interested in.
click on calculate and the calculator tells you the estimated amount you would have to pay in that year.
for example:
i entered 1914, 1, 2005, and the calculator told me 19.53.
that's pretty close to 21.43 that you were given.
it's not right on, but you don't expect it to be, because it's an estimate with an error factor plus or minus that can be large or small depending on how well the data fits the curve that was established to estimate it.
a straight line estimate is just another curve that's established to fit the data as well as it can.
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