SOLUTION: In favourable BREEding conditions , a colony of insects can multiply 10 fold every three weeks. IF there are now 500 insects in the colony, express the number of insects N as a fu

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: In favourable BREEding conditions , a colony of insects can multiply 10 fold every three weeks. IF there are now 500 insects in the colony, express the number of insects N as a fu      Log On


   

Question 805686: In favourable BREEding conditions , a colony of insects can multiply 10 fold every three weeks. IF there are now 500 insects in the colony, express the number of insects N as a function of elapsed time W weeks.
Can you please help me out? Thanks so much in advance:)
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
I = initial pop
P = resulting pop in three weeks
P=I%2Ae%5E%28kw%29, w is number of weeks.
10=1%2Ae%5E%28k%2A3%29 keeping the time unit as weeks.

ln%2810%29=3k%2Aln%28e%29
ln%2810%29=3k
highlight%28k=%281%2F3%29ln%2810%29%29

You wanted to call the population , N, so say
N=500e%5E%28kw%29, but you would still want to compute k before finishing the function.