# Math

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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 -

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 -

I made a mistake. after eight days , its 199.99 spiders.

I still don't understand how would we get s?

• Math -

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 -

Ohh all i needed to do was divide! heh thanks a lot!

• Math -

You're welcome!

• Math -

you guys never gave an answer..

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