Question 974849
y=ab^x is the basic form.  When x is increased by 16 days, y triples.  6377292/236196  = almost 27.  That is tripling three times
y=a(1+r)^x
a=where it starts
y/a=(1+r)^x
but y/a=3
3=(1+r)^x
Take ln both sides
ln3= x ln (1+r)
1.1=16 ln (1+r)
0.06875=ln (1+r)
raise both to the e power
1.0711=1+r
r=0.0711, the rate of increase.

236296 (1+0.0711)^x  ;;is the basic equation.
6377292=236296 (1+0.0711)^x
Divide to get 26.989=1.0711^x
ln of both sides  ;; 3.295=x ln 1.0711   ;;; divide by the ln, which is 0.0687
3.295/0.0687 =x ; x=47.96 days or 48 days.  

The tree population increases by a factor of 4 in how many days?
ln4=x (ln(1+.0711);;;  1.386=x *0.0687=20.175 days.
It has quadrupled twice and a little more.  You can get that de novo by noting it increased by a factor of 27, which is 2 quadruplings but not three.

2,000,000,000=236296 (1.0711)^x
divide out  and get  843696=1.0711^x
take logs both sides  9.0435=x (.0687);  x= 131.63 days.  Note, rounding will make a difference here.

Does this make sense?  I get a rough count of 8 triplings, which would be 128 days.  Yes, this makes sense.

4=236296(1+.0711)^x
0.00001693=1.0711^x
-10.98= 0.0687 *x
x=160.
Therefore, it was 160 days ago.

That would be 10 triplings.  Or 3^10.  4*(3^10)=236296.

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18921*(0.75)^x;; x=7
0.75^7= 0.1335
18921*0.1335=2525.65 or 2526 trees

You can do this for x^8, x^9, etc.
or 18921*(0.75)^x=99
99/18721=0.00523
ln(0.00523)=x ln (0.75)
-5.253= x (-0.288)
x= 18.26 weeks.