The populations of termites and spiders in a certain house are growing exponenti

Question

The populations of termites and spiders in a certain house are growing exponentially. The house contains 90 termites the day you move in. After four days, the house contains 190 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.

How long (in days) does it take the population of spiders to triple? (Round your answer to one decimal place.)

(PLEASE DO NOT COPY OTHER ANSWERS AND POST THEM FOR ME!!!!)

Explanation / Answer

Intially 90 termites

after 4 days 190 termites

Let T be function of termites and S be function for spiders

functions for exponetial grwoth :T(x) = To(a)^x ; S(x) = So(b)^x

T(3) = 2S(3)    ;     T(8) = 4S(8)

T(3) = 2S(3) ---> To(a)^3 = 2*So(b)^3

T(8) = 4S(8) ---> To(a)^8 = 4So(b)^8

divide both equations : a^5 = 2b^5

Find a : T = To(a)^x ; 190= 90(a)^4

a= (19/9)^1/4 = 1.21

Now b = (a/2^1/5) = 1.05

So, Popoulation of spiders triple:

S(x) = 3S(0)

b^x = 3

1.05^x = 3

x = 22.52 = 22.5 days

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.