Someone please help me with this formula for exponential population growth. (P=Ae^kt)
See attached file please!

Question

Someone please help me with this formula for exponential population growth. (P=Ae^kt) 
See attached file please!

anonymous · Answer

I got it up until this point, no idea where the sub-a and a come from, or the "y" ....
please help

kc_kennylau · Answer

$\Large\log_aa^y=y$ is the definition of logarithm expressed in Mathematical notations

kc_kennylau · Answer

It means that the logarithm of a number to the power of another with base being the original number will have a value of the other.

anonymous · Answer

okay, how do I apply it?

kc_kennylau · Answer

The definition of $\ln x$ is just $\large\log_ex$

kc_kennylau · Answer

Therefore $\Large\ln e^{10k}=\log_ee^{10k}=10k$ (applying the definition in the last step)

anonymous · Answer

the letters are terribly confusing to an online student of an algebra 1 class. 
thank you

kc_kennylau · Answer

Do you get it now?

kc_kennylau · Answer

The "a" and the "y" are just dummy variables.

anonymous · Answer

working on it, give me a minute

anonymous · Answer

See, I am solving for k and my calculator is giving me a hard time.

kc_kennylau · Answer

anonymous · Answer

Didn't know google was a scientific calculator, lol! Thanks I had a laugh and it helped. I kept getting like 42.07788

kc_kennylau · Answer

Maybe you missed out some parentheses?

anonymous · Answer

maybe, the scientific calculator I was using was set up strangely! thank you I know how to do the rest of these questions now, ( I THINK!)

anonymous · Answer

What exactly does ln stand for?
It kind of just threw me into this whole subject with nearly no build up.

kc_kennylau · Answer

Can you tell me some more decimal places? I might be able to track.

In LN, the L stands for Logarithm and the N stands for Natural

kc_kennylau · Answer

LN is called Natural Logarithm

kc_kennylau · Answer

And I have no idea why they reverse the order

anonymous · Answer

that was all i kept written but i used google for everything else and it is coming up correct now when I click answers.

kc_kennylau · Answer

Nah, just give me more decimal places and I help you find what's wrong with your calculator

anonymous · Answer

Thank you very much. That was much appreciated. (:

kc_kennylau · Answer

Anytime!

anonymous · Answer

The notes define e as the natural logarithim base, does e need to be solved for specifically, or is it a specific value I can just plug in?