Question

The populations of termites and spiders in a certain house are growing exponentially. The house contains 110 termites the day you move in. After four days, the house contains 210 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.)
)

Answer 1

Let population of termites is given by A, ekst and that of spiders by Azeket Now given at t=0 population of termites allo - A e 4 xo = 110 - A = 110 and at t=4 A e 4x4 = 210 =) 110 e 4k = 210 => 64K4 = 210 =) K = 1 In (21) = 0.16 Now again at t=3 population of termites - 2 x population of spiders - A, ek X3 - 2 A ekzx30 - and similarly at t=8 A, eK X8 _ 4 A₂ ekz X 8 - 210 /10 Notes:

Suation ® - Equation > A 84 44208K2 A ek = 24₂ 83k2 eski = 265k2 eske = t - eski = 1 esxo.16 » Kz az ln (1012) = 0.021 Now, Let after days population of spiders will become triple - A etzt = 342 ekat =3 = t - t lu(3) = 52.3 days