SOLUTION: Johann has an antique printing press that he inherited from his grandfather.The printing press is currently worth $26 600, and it has been appreciating at a rate of 3% each year.
Algebra ->
Systems-of-equations
-> SOLUTION: Johann has an antique printing press that he inherited from his grandfather.The printing press is currently worth $26 600, and it has been appreciating at a rate of 3% each year.
Log On
Question 1037471: Johann has an antique printing press that he inherited from his grandfather.The printing press is currently worth $26 600, and it has been appreciating at a rate of 3% each year. Use a graphical model of the problem to predict how many years will it take for the value of the printing press to double.
Thanks so much :) Found 2 solutions by Theo, josmiceli:Answer by Theo(13342) (Show Source):
the value when x = 0 is 26600 * 1.03^0 = 26600.
the value when x = 1 is 26600 * 1.03^1 = 27398.
you can solve for when it will double by formula as follows:
2 * 26600 = 53200.
formula becomes 53200 = 26600 * 1.03^x.
divide both sides of this equation by 26600 to get 2 = 1.03^x.
2 = 1.03^x is the formula you would use.
take the log of both sides of this equation to get log(2) = log(1.03^x).
log(1.03^x) is equivalent to x * log(1.03)
formula becomes log(2) = x * log(1.03)
divide both sides of the equation by log(1.03) and solve for x to get x = log(2) / log(1.03).
your solution should be x = 23.44977225 years.
graphically, you would graph the function of y = 26600 * 1.03^2.
you would also graph y = 53200.
the intersection of the two equations will be the solution.
the graph looks like this:
the graph shows that the intersection of the two equation occurs when x = 23.45.
that's the same answer you got by formula after it is rounded to two decimal places.
You can put this solution on YOUR website! You need to plot some points, , value
on the vertical axis, and time in years
on the horizontal axis
-----------------------
The equation is:
where
-------------------
This is the point ( 0, 26600 )
--------------------------
This is the point ( 1, 27398 )
---------------------------
----------------------------
keep adding points and try to predict the
year, when
------------------------------
Here's the actual plot up to about years
so you can cheat a little:
