The current population of a small town is 5062 people. It is believed that town's population is tripling every 11 years. Approximate the population of the town 7 years from now.

Question

The current population of a small town is 5062 people. It is believed that town's population is tripling every 11 years. Approximate the population of the town 7 years from now.

Answer 1

I. Do you remember the population growth function?

Population usually uses exponential growth model, then the time required for the original size to 2x, 3x... etc

Here is the general population growth model:

y=y₀e^kt, where y= final population, y₀= initial population (5062), k=growth factor, t= time

y=5062e^kt

II. Find growth factor

We know that population triples in 11 years. We can find growth factor from this information.

For the final population to triple:

y=3y₀

and let T=time for the final population to triple

y=y₀e^k

3y₀ = y₀e^kT

Let's do the pleasure of eliminating common term (y₀)on both sides:

3 = e^kT, where T=11 years

Finding k

ln(3)/11=k

III. Plug k into general population equation

y=5062e^kt

where k= ln(3)/11

y=5062e^(ln(3)/11)t

where the year in question is 7, so t=7

y=5062e^{(ln(3)/11)(7)}

y= 10184

The town's population 7 years from now is 10,184 people.