Answer:
From the question,
[tex]\begin{gathered} P_0=9 \\ r=0.4 \end{gathered}[/tex]The formula for the growth rate will be calculated using the formula below
[tex]\begin{gathered} F=P(1+r)^n \\ F=\text{future value} \\ P=present\text{ value} \\ r=\text{growth rate} \\ n=nu\text{mber of times per period} \end{gathered}[/tex]In,
[tex]\begin{gathered} P_0,n=0 \\ P_1,n=1 \\ P_2,n=2 \\ P_9,n=9 \end{gathered}[/tex]Given that
[tex]\begin{gathered} P_0=9 \\ F=P(1+r)^n \\ P_0=9(1+0.4)^0 \\ P_0=9\times1 \\ P_0=9 \end{gathered}[/tex][tex]\begin{gathered} F=P(1+r)^n \\ P_1=9(1+0.4)^1 \\ P_1=9\times1.4 \\ P_1=12.6 \end{gathered}[/tex]Hence,
P1 = 12.6
Also, we will have P2 to be
[tex]\begin{gathered} F=P(1+r)^n \\ P_2=9(1+0.4)^2 \\ P_2=9\times1.4^2 \\ P_2=17.64 \\ P_2\approx1\text{ decimal place} \\ P_2=17.6 \end{gathered}[/tex]Hence,
P2 = 17.6
Therefore,
The formula for Pn will be represented below as
[tex]\begin{gathered} P_n=9(1+0.4)^n \\ P_n=9(1.4)^n \end{gathered}[/tex]The explicit formula for Pn will be
[tex]P_n=9(1.4)^n[/tex]To figure out the values of P9. we will substitute the value of n=9 in the equation below
[tex]\begin{gathered} P_n=9(1.4)^n \\ P_9=9(1.4)^9 \\ P_9=185.9 \end{gathered}[/tex]Hence,
P9 = 185.9
