Question 995494: 1.A city's current population is 158,144. If this represents an increase of 85% of the population 7 years ago, what was the city's population 7 years ago?
2.The value of a currency appreciated by 25.60% of its value last month and then depreciated by 25.60% this month. By what percent did the currency appreciate or depreciate over the 2-month period?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! question 1:
current population is 158,144.
this represents an increase of 85% of the population 7 years ago.
x + .85 * x = 158144
1.85x = 158144
x = 158144/1.85 = 85483.
population 7 years ago was 85483.
question 2:
x = value 2 months ago.
y = value 1 month ago.
z = current value.
x + .256 * x = y
y - .256 * y = z
in the second equation for z, replace y with the value of y from the first equation for y.
you get:
z = y - .256 * y becomes:
z = (x + .256 * x) - .256 * (x + .256 * x)
simplify this to get:
z = 1.256 * x - .256 * (1.256 * x)
simplify further to get:
z = 1.256 * x - .321536 * x
combine like terms to get:
z = .934464 * x
this means that the value of the current month is equal to .934464 * the value of 2 months ago.
.934464 is equal to 1 - .065536.
z = .934464 * x is therefore equivalent to z = x - .065536 * x.
your net gain is equal to - .065536 * x which means that your net loss is equal to .065536 * x.
.065536 * 100 is equal to 6.5536%.
your value has depreciated by 6.5536%.
put this into numbers and it's easier to see what i mean.
you start with 1000, for example.
in one month, that appreciates 25.6% to become equal to 1000 + .256 * 1000 = 1256
in another month that depreciates 25.6% to become equal to 1256 - .256 * 1256 = 934.464
you started with 1000 and you ended with 934.464.
you took a net loss of 1000 - 934.464 = 65.536
that's a net loss percent of 65.536 / 1000 = .065536 * 100 = 6.5536%.
|
|
|
