can someone help?

3.On January 1, 2010 chessville has a population of 50,000 people. Chessville then enters a period of population growth, its population increases 7% each year, on the same day Brookeville has a population of 70,000 people, Brookeville starts to experience a population decline. its population decreases 4% each year.

During what year will the population of Chessville first exceed that of Brookeville? show all your work.

Question

can someone help?

3.On January 1, 2010 chessville has a population of 50,000 people. Chessville then enters a period of population growth, its population increases 7% each year, on the same day Brookeville has a population of 70,000 people, Brookeville starts to experience a population decline. its population decreases 4% each year. 

During what year will the population of Chessville first exceed that of Brookeville? show all your work.

anonymous · Answer

let work it out step by step

anonymous · Answer

okay

anonymous · Answer

what do think the equation of increase in population for chessville is?

anonymous · Answer

50,000+ 7%= ?

anonymous · Answer

70,000 - 4%= ?

anonymous · Answer

I will calculate it for the first 3 years, and you will figure it out because I know that u're smart!

anonymous · Answer

haha not really XD 
im extremely bad at math

anonymous · Answer

year1=50000*1.07; year2=50000*(1.07)^2; year3 50000*(1.07)^3....

anonymous · Answer

what do you think the general form will be?

anonymous · Answer

(1.07)^4 and keep adding the exponent by 1??

anonymous · Answer

r u homeschooled?

anonymous · Answer

yeah i am

anonymous · Answer

yes

anonymous · Answer

so the population of chessville after x years will be 50000*(1.07)^x

anonymous · Answer

now think of the same thing for brookeville

anonymous · Answer

but this time it'is a population decrease, so instead of adding 0.07 to 1 we're going to ...?

anonymous · Answer

how did you get (1.07)??

campbell_st · Answer

you need to equate 

Growth = Decline 
so 

$$50000 \times 1.07^n = 70000 \times 0.96^n$$

you need to solve for n, the time periods...

or an alternative is to graph 

$$C(x) = 50000 \times 1.07^x$$

and 

$$B(x) = 70000 \times 0.96^x$$

hope it helps

anonymous · Answer

what does increasing by 7% means? it means 100%*50000+7%*50000=50000*(107%)=50000*(1.07)

campbell_st · Answer

the growth is 7% per year... 

so the new population = old population + 7%
                    1.07         =         1             + 0.7

anonymous · Answer

"Math is easy once you take it easy"-Xesevoli

anonymous · Answer

i wish i was smarter XD 
....this is sad

anonymous · Answer

Believe me it isn't 'bout being smarter

anonymous · Answer

i guess.. well thanks for the help :D  
@Xesevoli  @campbell_st

anonymous · Answer

You're welcome, and if ever you wanted to "learn" how to solve "math"  I will be here!

Ciao!