Population Growth Activity
Goal: Use compound, exponential and logistic growth models to predict population size and doubling time, solve percentage-growth word problems, and explain the effect of carrying capacity.
What to do
- In the word-problem solver further down the page, press “20,000 at 12%/yr → 210,000”. Record the time to reach N and the answer shown for a continuous rate.
- Press “1,100 doubling every 60 yr, in 180 yr” and record the population after 180 years.
- Press “6.17 billion, r = 0.013”. Record the doubling time for a continuous rate and the rule of 70 estimate.
- Scroll back up to the growth-curve calculator and press “Rabbits on an island” (logistic growth, K = 2,000). Record N after 15 years, then set Time t to 5 and record N again.
Record your results
| What to find | Your result |
|---|---|
| Years for 20,000 to reach 210,000 at 12% per year | |
| The same problem if 0.12 is a continuous rate | |
| Population of 1,100 after 180 years, doubling every 60 years | |
| Doubling time if r = 0.013 is a continuous rate | |
| Rule of 70 estimate for 1.3% per year | |
| Rabbits on an island: N after 15 years | |
| Rabbits on an island: N after 5 years |
Questions
Write the equation for the town problem using N = N₀(1 + r)^t, then show how taking logarithms gives the time. Round to the nearest year.
Why is the continuous-rate answer (N = N₀e^(rt)) shorter than the compound answer for the same 12%?
A town of 1,100 doubles every 60 years. Without the calculator, explain why it has 8,800 people after 180 years.
The rule of 70 says doubling time ≈ 70 ÷ (percent growth rate). How close is it to the exact answer for a continuous rate r = 0.013, and why does it work?
Compare the rabbit population after 5 and after 15 years. Why does it grow so much in the first 5 years but barely change after 15? Use the term carrying capacity.
Challenge: logistic growth is fastest at N = K/2. For the rabbits, about when is that, and what is the fastest growth rate rK/4?
Free from Biology Lab · thebiologylab.org · HS-LS2-1: Use mathematical representations to support explanations of factors that affect the carrying capacity of ecosystems.