PLEASE HELP ..

On January 1 2010, Chessville has a population growth. Its population increases 7% each year. On the same day checkersville has a population of 70,000 people. Cheakersveille starts to expeirence a population decline . It's population decreases 4% each year . During what year will the population of Chessville first exceed that of Checkersville?

Question

PLEASE HELP ..

On January 1 2010, Chessville has a population growth. Its population increases 7% each year. On the same day checkersville has a population of 70,000 people. Cheakersveille starts to expeirence a population decline . It's population decreases 4% each year . During what year will the population of Chessville first exceed that of Checkersville?

anonymous · Answer

we are missing the initial population of "chessville"

anonymous · Answer

oh sorry its 50000

anonymous · Answer

$$50000(1.07)^t=70,000(.96)^t$$ solve for $t$

anonymous · Answer

lets see, divide by $50,000$ get 
$$(1.07)^t=1.4(.96)^t$$ divide by $(.96)^t$ get 
$$\left(\frac{1.07}{.96}\right)^t=1.4$$

anonymous · Answer

then use "change of base" formula to find $t$
$$t=\frac{\ln(1.4)}{\ln(\frac{1.07}{.96})}$$

anonymous · Answer

and of course a calculator

anonymous · Answer

https://www.wolframalpha.com/input/?i=log%281.4%29%2Flog%281.07%2F.96%29