Posted by SC on Thursday, November 5, 2009 at 8:17pm.
The population of termites and spiders in a certain house are growing exponentially. the house contains 100 termites the day you move in. After 4 days, the house contains 200 termites. Three days after moving in, there are two times as many termites as spiders. Eight days after moving in, there were four times as many termites as spiders/ Hows long in days does it take the population of spiders to triple?
What I done so far.
TERMITES
y(not)=100
t=4
y=200
200=100b^4
b=2^(1/4)
T(t)=100(1.189207)^t
for the spiders.S(t).. i tried plugging t=3 and t=8and divided by two and four to the T(x) equation.... and for two numbers 84.089 and 99.99..... but I think Im doing it wrong
or is it
T(t) = 2(S(t))?

Math  TeacherJim, Thursday, November 5, 2009 at 8:47pm
I agree with your first part: b=2^(1/4) = 1.189207.
Now, after 3 days, according to the question, we must have 84.089 spiders  wonder what .089 of a spider looks like?  and after 8 days, we have 100.
If S0 is the number of spiders on day zero, and s is the multiplication rate of spiders, then
S0 * s^3 = 84.089
S0 * s^8 = 100
From which we can quickly get s^5.
And then we get s.
And from there, there's not much left to do, I think.

Math  SC, Thursday, November 5, 2009 at 8:57pm
I made a mistake. after eight days , its 199.99 spiders.
I still don't understand how would we get s?

Math  TeacherJim, Thursday, November 5, 2009 at 9:07pm
You didn't make a mistake:
"Eight days after moving in, there were four times as many termites as spiders"
But 100 * (2^.25)^8 = 400 (termites)
So if there were 400 termites, there were 100 spiders.
So how do we get s?
S0 * s^3 = 84.089
S0 * s^8 = 100
(S0 * s^8) / (S0 * s^3)
= s^5
= 100 / 84.089
s = (100 / 84.089)^(1/5)

Math  SC, Thursday, November 5, 2009 at 9:10pm
Ohh all i needed to do was divide! heh thanks a lot!

Math  TeacherJim, Thursday, November 5, 2009 at 9:13pm
You're welcome!

Math  nissreen, Thursday, January 10, 2013 at 7:43pm
you guys never gave an answer..
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