Doubles every 8 years? It is not 12.5%
Get the yearly growth rate in one line, then read the year off a crossing.
1:37 · Nonlinear Functions
Worked in this video
A population doubles every 8 years. It is modeled by P = P₀ · 2^(t/8), where t is in years.
By what percent does the population grow each year, to the nearest tenth?
On paper this means rewriting 2^(t/8) as (2^(1/8))^t and then finding an eighth root without a calculator, which is why the tempting guess is 100% ÷ 8 = 12.5%. That is wrong, because growth compounds. The yearly factor is 2^(1/8): type exactly that into Desmos and it reads 1.0905. Subtract 1 and multiply by 100: the population grows 9.1% a year.
Answer: 9.1%