Harison ,
[tex3]\text{P(t)} = 2.000.(1,1)^{\text{t}}[/tex3]
Para [tex3]\text{P(t)}=22.000[/tex3]
[tex3]22.000 = 2.000.(1,1)^{\text{t}}[/tex3]
[tex3]11=(1,1)^{\text{t}}[/tex3]
[tex3]\log11=\log(1,1)^{\text{t}}[/tex3]
[tex3]\log11=\text{t}.\log(1,1)[/tex3]
Perceba que [tex3]1,1=\frac{11}{10}[/tex3]
[tex3]\log11=\text{t}.\log\left(\frac{11}{10}\right) [/tex3]
[tex3]\log11=\text{t}.(\log11-\log10) [/tex3]
Substituindo [tex3]\log11=1,04[/tex3]
e [tex3]\log10=1[/tex3]
[tex3]1,04=\text{t}.(1,04-1) [/tex3]
[tex3]{\color{red}\boxed{\text{t}=26 \text{ meses}}}[/tex3]