Posted by **Maria** on Monday, October 17, 2011 at 7:37pm.

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

- Math: Calculus -
**bobpursley**, Monday, October 17, 2011 at 8:19pm
changing the base of a log: Alg II

http://www.sosmath.com/algebra/logs/log4/log43/log43.html

- Math: Calculus -
**Maria**, Monday, October 17, 2011 at 8:29pm
I'm sorry, I still don't understand

- Math: Calculus -
**Steve**, Tuesday, October 18, 2011 at 12:25am
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

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