we have the equation
[tex]P(t)=319(2)^{(\frac{t}{3})}[/tex]
For P(t)=2,552
substitute in the given equation
[tex]2,552=319(2)^{(\frac{t}{3})}[/tex]
solve for t
[tex]\begin{gathered} 2,552=319(2)^{(\frac{t}{3})} \\ \frac{2,552}{319}=(2)^{(\frac{t}{3})} \end{gathered}[/tex]
Apply log both sides
[tex]\begin{gathered} \log \lbrack\frac{2,552}{319}\rbrack=\log \lbrack(2)^{(\frac{t}{3})}\rbrack \\ \log \lbrack\frac{2,552}{319}\rbrack=\frac{t}{3}\cdot\log (2) \end{gathered}[/tex]
t=9 years
the answer is 9 years from the time of introduction
