Bonsoir,
Ex_2:
[tex]p_0=8000\\
p_1=0.9*p_0+400\\
p_2=0.9*p_1+400\\
=0.9^2*p_0+0.9*400+400\\
=0.9^2*p_0+400*(0.9+1)\\
=0.9^2*p_0+400* \dfrac{0.9^2-1}{0.9-1} \\
=0.9^2*p_0-4000*(0.9^2-1)\\
[/tex]
[tex]p_3=0.9*p_2+400\\
=0.9^3*p_0+0.9^2*400+400*0.9+400\\
=0.9^3*p_0+400*(0.9^2+0.9+1)\\
=0.9^3*p_0+400* \dfrac{0.9^3-1}{0.9-1} \\
=0.9^3*p_0-4000*(0.9^3-1)\\
p_{n}=0.9*p_{n-1}+400\\
=0.9^n*8000-4000* \dfrac{0.9^n-1}{0.9-1} \\
=0.9^n*8000-4000*0.9^n+4000\\
=0.9^n*4000+4000\\ [/tex]
4000*(0.9^n+1)<6000
==> 0.9^n+1<1.5
==>n*ln(0.9)>ln(0.5)
==>n>ln(0.5)/ln(0.9)
==>n>6.57881....
==>n=7
