Solve growth/decay models for time using logarithms
Solve A0(1 +- i)^t = A0*M for t using logarithms, applied to a tech growth or decay context. Unlimited questions, five difficulty levels, and a full worked solution every time — free.
Try one
The view count on a coding tutorial channel grows by 10% every week. About how many weeks (to one decimal place) until it triples?
1.1t = 3
Answer: 11.5
See one solved, step by step
A startup's active user count grows by 4% every month. About how many months (to one decimal place) until it triples?
1.04t = 3
📘 Worked solution
11.04t = 3Growing 4% per month means multiplying by 1.04 each time, so after t months the total has been multiplied by 1.04^t.
2t · log(1.04) = log(3)Take the logarithm of both sides and use the power law to bring the exponent t down in front.
3t = log(3) / log(1.04) = 1.0986 / 0.0392Divide to isolate t.
4t ~ 28 monthsRound to one decimal place.
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