A city doubles its population in 25 years. If it is growing exponentially, when will it triple its population?
The above is a question in my maths textbook in the topic Exponential Growth & Decay.
I'm a bit confused as to how I should approach this question.
We have been taught to use the formula:
$$Q=Ae^{kt}$$
Where $Q$ is the quantity, $A$ is the initial quantity, $k$ is the growth/decay constant and $t$ is the time.
In reference to the question, I don't think I need $A$ so here is the equation I ended up with:
$$2Q=e^{25k}$$
Edit:
I found out that $$k=\frac{\ln2}{25}$$
I then let $Q=3A$ and the following is my working:
$$3A=Ae^{25\frac{\ln2}{25}t}$$
$$3A=Ae^{\ln2t}$$
$$3=e^{\ln2t}$$
$$3=2^{t}$$
$$\ln{3}=t\ln{2}$$
$$t=\frac{\ln{3}}{\ln{2}}$$
$$t=1.6$$
I can't figure out what is wrong in my working out.
The provided answer is: 39.6 years
Best Answer
Start with $Q = Ae^{kt}$. If the doubling time is 25 years, this translates to $$2A = Ae^{25k}.$$ You should be able to solve for $k$ and make a go of it now.