Population Prediction

Algebra 2 · Axiom Academy

One relationship — P = P₀(1 + r) t — decides every growing population. Logarithms are how you solve it for time. Riverside started 2020 with 5,000 people , growing 3% a year — the town planners need to know exactly when it crosses 10,000 . Set a growth rate and press Grow — watch the population compound, year after year, for two decades. That's P = P₀(1 + r) t , live. Flip the question around: pick a growth rate, and read off how many years it takes Riverside to double from 5,000 to 10,000 — the exponent, unlocked by logarithms. Is chasing a higher rate worth it? You're planning around 3% growth and need about 23 years. How much does pushing the rate higher actually buy you? Drag and watch the years saved — notice each extra point buys less than the last. The same move works everywhere growth compounds — log(target ÷ start) ÷ log(1 + rate) finds the time: a bacteria culture hitting 10,000 in 19.93 hours , savings doubling at 7% in 10.24 years (the Rule of 72), a fossil's carbon-14 falling to 25% in exactly 11,460 years .

This is the written version of the interactive lesson above. See the full Algebra 2 course.