Growth models quiz
Reveal-answer practice comparing linear, exponential, and logistic growth, plus the Rule of 70.
Open quizLearn the Concepts
1 · Linear vs. exponential growth
- Linear growth adds a fixed amount each period (saving $50 a month). A straight line.
- Exponential growth multiplies by a fixed percentage each period (a population growing 5% a year). It curves upward ever more steeply.
The future value after t periods of exponential growth is:
A = P · (1 + r)t (or repeated doubling: A = P · 2(number of doublings))
Learn the Concepts
2 · Doubling time and limits to growth
The Rule of 70 gives a quick estimate of how long an exponentially growing quantity takes to double:
doubling time ≈ 70 ÷ (percent growth rate)
Real growth can't continue forever. Logistic growth starts out roughly exponential, then slows and levels off at the environment's carrying capacity — the maximum the resources can sustain. Its graph is an S-shaped curve.
Worked Examples
See it done, step by step
Example 1 — 50 spores double every 6 hours. How many after 24 hours?
First count the doublings: 24 ÷ 6 = 4.
A = 50 × 24 = 50 × 16 = 800 spores.
Example 2 — An investment grows 5% per year. Estimate its doubling time.
Use the Rule of 70.
70 ÷ 5 = about 14 years.
Example 3 — $500 grows 8% per year. How much after 3 years?
Use A = P(1 + r)t.
A = 500 × (1.08)3 = 500 × 1.259712 ≈ $629.86.
Watch & Review
Resources for this module
Growth in action
Slides + calculators
Check Yourself
Quick self-check
1. A population grows 7% per year. Estimate its doubling time.
70 ÷ 7 = about 10 years.
2. Saving exactly $100 every month — linear or exponential?
Linear — a constant amount is added each period.
3. What does carrying capacity describe?
The maximum population the environment can sustain, where logistic growth levels off.
Ready to turn it in?
When growth models make sense, complete the Module 11 homework and quiz in Canvas. This wraps up the material for Test 3.
Submit in Canvas