# Problem solving

• Feb 6th 2011, 01:48 PM
melvis
Problem solving
I just want to make sure that I got the right answer.
http://img843.imageshack.us/img843/1864/39389663.png

that's how I found A since, C is the limit I plugged 100,000 for it. B is the growth rate and it's 1 as mentioned. now to find a, I just plugged it the initial pop when time was 0.
100=100,000/(1+ae^-0*1)
100(a+1) = 100,000
100a +100 = 100,000
100a = 99,900
a=99,900/100
a= 999
therefore, the final equation is
p(t) = 100,000/(1+999e^-t)

just want to make sure that I got it right, thx for your help.
• Feb 6th 2011, 01:51 PM
dwsmith
Quote:

Originally Posted by melvis
I just want to make sure that I got the right answer.
http://img843.imageshack.us/img843/1864/39389663.png

that's how I found A since, C is the limit I plugged 100,000 for it. B is the growth rate and it's 1 as mentioned. now to find a, I just plugged it the initial pop when time was 0.
100=100,000/(1+ae^-0*1)
100(a+1) = 100,000
100a +100 = 100,000
100a = 99,900
a=99,900/100
a= 999
therefore, the final equation is
p(t) = 100,000/(1+999e^-t)

just want to make sure that I got it right, thx for your help.

Take the limit as t goes to infinity.
• Feb 6th 2011, 01:58 PM
melvis
Quote:

Originally Posted by dwsmith
Take the limit as t goes to infinity.

It stays at 100,000 where it should stay ? I'm assuming that's a way to check this kind of problem, right?
• Feb 6th 2011, 02:03 PM
pickslides
Correct.
• Feb 6th 2011, 02:03 PM
dwsmith
Quote:

Originally Posted by melvis
It stays at 100,000 where it should stay ? I'm assuming that's a way to check this kind of problem, right?

It says the island can hold no more than 100,000 so you are correct or made an error that yields the same results. The odds are in your favor on being correct though.
• Feb 6th 2011, 02:10 PM
melvis
Thx for the help ;).

Quote:

Originally Posted by dwsmith
It says the island can hold no more than 100,000 so you are correct or made an error that yields the same results. The odds are in your favor on being correct though.

• Feb 6th 2011, 02:12 PM
dwsmith
Quote:

Originally Posted by melvis
Thx for the help ;).

Your welcome. Whenever you know the maxium number whether it be population, bacteria, etc, you can take the limit as t,x, ... goes to infinity. It would be extremely rare that a mistake will allow you to obtain the correct limit.