Thread: exponential growth

The question is if the population takes 20 years to triple, how many years does it take to double.

We know that the population in 20 years ( ) is triple the starting one ( ):


It follows that

and
.

Now set up equation for doubling in unknown time:


and get from that

Is this the actual equation given to you?

Does y' represent a derivative here?

EDIT: Is k a constant or is it the time in years?

That is the actual question, and k is a constant. The equation was made by me from my interpretation.

Okay, then a more appropriate equation would be:



Then you say, when t = 20 years, the population y is 3 times that of the initial population y_o



This gives you

And then you continue like courteous did.

Exponentials to all bases and logarithms to all bases are interchangable. I prefer to avoid "e" in favor of an obvious base.

Saying that a population take "T" years to triple is the same as saying it is given by since "t/T" is the number of times it triples. So asking for the number of years to double is asking form t such that . Divide both sides by C and take the logarithm (to any convenient base) of both sides: (t/T)log(3)= log(2), t= T (log(2)/log(3)).

Here, T= 20 so the time to double is 20 (log(2)/log(3)).