Math: Calculus
posted by Maria .
Assume that a population size at time t is N(t) and that N(t)=40 x 2^t , t>0.
Show that N(t)=40e^t ln2
Can someone please guide me step by step on this question? Im really confused. thanks.
I tried to work it out, and this is what I got.
N(t)= 40 x 2^t
= 40 x ln 2^t
= 40 x t ln 2

changing the base of a log: Alg II
http://www.sosmath.com/algebra/logs/log4/log43/log43.html 
I'm sorry, I still don't understand

by definition, 2 = e^(ln 2)
Therefore, 2^t = e^(ln 2)^t = e^(t ln 2)
Make sense yet?
Now, ln (2^t) = t * ln 2
So, ln N = ln 40 + t ln 2