SOLUTION: The population is decreasing at a rate of 2% per year. If the population is 27,200 today, what will the population be in 10 years? Round your answer to the nearest whole number, if

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The population is decreasing at a rate of 2% per year. If the population is 27,200 today, what will the population be in 10 years? Round your answer to the nearest whole number, if      Log On


   

Question 1071612: The population is decreasing at a rate of 2% per year. If the population is 27,200 today, what will the population be in 10 years? Round your answer to the nearest whole number, if necessary.

Would you please help me solve this? i missed this day in class and cannot solve it or even try to begin. thank you in advance!
Found 2 solutions by josgarithmetic, Edwin McCravy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Decrease of 2% each year means keeping 98% each year.


y=p%2Ae%5E%28kt%29
y population
p initial population
t time in years

In one year,
98=100e%5E%28k%2A1%29, assuming if starting with population 100;
ln%2898%29=ln%28100%2Ae%5Ek%29
ln%2898%29=ln%28100%29%2Bk%2Aln%28e%29
k%2A1=ln%2898%29-ln%28100%29
k=ln%2898%29-ln%28100%29
k=-0.0202
MODEL: highlight_green%28y=27200%2Ae%5E%28-0.0202t%29%29


What is the population in 10 years?
t=10; find y.
y=27200%2Ae%5E%28-0.0202%2A10%29
y=27200%2Ae%5E-0.2020
To the nearest WHOLE number, y=22225

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
It's a geometric sequence with first term = a1=27200, and since
a decrease of 2% each year means that each year it is only 98% of
what it was the year before.

So:
 
the 2nd yesr it'll be worth (0.98)(27200) = $26656.00
the 3rd yesr it'll be worth (0.98)2($27200) = $26656.00
the 4th yesr it'll be worth (0.98)3($27200) = $26122.88
...

So

the nth yesr it'll be worth (0.98)n-1($27200)

a1 = the first term
a2 = the second term
...
an = the nth term

a%5Bn%5D=a%5B1%5Dr%5E%28n-1%29

You want the 10th term.

a%5B10%5D=27200%2A0.98%5E%2810-1%29

a%5B10%5D=27200%2A0.98%5E9

a%5B10%5D=22677.93913

Round to $22678

Edwin