Réponse :
Bonjour,
Explications étape par étape :
Soient C le capital, t le taux
[tex]C_0=C\ (ann\'ee\ 0)\\\\C_1=C+C*\dfrac{t}{100} =C*(1+\dfrac{t}{100} )\\\\C_2=C*(1+\dfrac{t}{100} )+C*(1+\dfrac{t}{100} )*(1+\dfrac{t}{100} )=C*(1+\dfrac{t}{100} )^2\\\\C_3=C*(1+\dfrac{t}{100} )^3\\\\C_4=C*(1+\dfrac{t}{100} )^4\\\\C_5=C*(1+\dfrac{t}{100} )^5\\\\On\ a:2*C=C*(1+\dfrac{t}{100} )^5\\\\2=(1+\dfrac{t}{100} )^5\\\\ln(2)=5*ln(1+\dfrac{t}{100})\\\\ln(1+\dfrac{t}{100})=\dfrac{ln(2)}{5} \\\\\dfrac{t}{100} =e^{\frac{ln(2)}{5}}-1\\[/tex]
[tex]\\\boxed{t=100*e^{\frac{ln(2)}{5}}-1}\\\\t\approx{14.8698354997...}[/tex]
