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Logarith help!

A colony of fast-breeding fish is introduced into a large, newly-built pond. The number of
fish in the pond, n, after t weeks is modelled by
n = 18000/ 1+ 8c^-t where c is the cube root of 2.

find the time taken for the initial population of fish to double in size, giving your
answer to the nearest day.

Reply 1

DestinySky

First you want to substitute t=0 to find the inital number
Then double this number and set n to this.
Then just rearrange to find t.

Reply 2

phoebeisgreat

Original post by DestinySky

First you want to substitute t=0 to find the inital number
Then double this number and set n to this.
Then just rearrange to find t.

yeah, i know but try it out-you get that 8c^-t =0 and how do you solve this??

Reply 3

joostan

Original post by phoebeisgreat

yeah, i know but try it out-you get that 8c^-t =0 and how do you solve this??

Just to clarify, is that:

n=\dfrac{18000}{1+8 (\sqrt[3]{2})^{-t}}

?

In which case I disagree. Can I see what you did, so I can find out where you went wrong?

(edited 8 years ago)

Reply 4

DestinySky

Original post by phoebeisgreat

yeah, i know but try it out-you get that 8c^-t =0 and how do you solve this??

I got (c^-t) - 7/16 = 0 , I think that's right. You need another term in the equation to solve it, did you remember to multiply the whole of the bottom of the fraction by 2n and not just the bit with c in it?