Mathematics from zero
Growth: free-recall review
Recall sticks better than re-reading. For each prompt, say or write a full answer from memory first — then open the model answer and check it against yours. The effort of pulling it from memory is what makes it last.
Reconstruct the unit’s core ideas from memory — the difference between adding and multiplying, why exponential growth overtakes linear, what a logarithm is, why the base matters, and why the log grows so slowly.
- 01What is the difference between linear growth and exponential growth?
- 02Why does exponential growth always overtake linear growth in the long run, even if it starts slower?
- 03What is a logarithm, and how does it relate to an exponent?
- 04Why is the base written with every logarithm — why does it matter?
- 05Why does a logarithm grow so slowly, and what makes that useful?
- 06Work out log₂(64) and log₁₀(1000), and explain what each answer counts.
If you could rebuild each answer from memory, you hold the unit’s spine: linear growth adds a fixed amount, exponential growth multiplies by one, and multiplying always overtakes adding in the long run. A logarithm reverses an exponent — log₂(N) is the exponent on 2 that reaches N, written with its base because the base sets the question. The log grows by just 1 per doubling, which is why it stays a small, calm scale for measuring explosive growth.