I'm trying to solve the following mathematical dilemma:
On the 1st of July 2000 a Lizard bears 4 babies. On the 1st July 2001 each of those Lizard bears in turn 4 babies. And so on. Assumed that each Lizard lays eggs once in its life, how many Lizards are born on the 1st July 2006 ?
I'd assume the result is 4^7 = 16384
Is it correct? Also, I wonder if the Fibonacci sequence can be used for the resolution of this dilemma?
Yes, it is $4^7=16384$ The exponent is just the year minus $1999$
The Fibonacci sequence does not play into it because the recurrence is just $a_{n+1}=4a_n$, which is different from the one in Fibonacci.