Question

Is someone able to explain the process of how to find the last 2 values??

Answer 1

as "t" increases, notice, the P is also increasing from its previous value, since that's the case, then is a "growth" equation,


`\bf \qquad \textit{Amount for Exponential Growth}\\\\ P=I(r)^t\qquad \begin{cases} P=\textit{accumulated amount}\\ I=\textit{initial amount}\\ r=rate\\ t=\textit{elapsed time}\\ \end{cases}\\\\ -------------------------------\\\\ \textit{we know that } \begin{cases} t=0\\ P=4 \end{cases}\implies 4=I(r)^0\implies 4=I\cdot 1\implies 4=I \\\\\\ therefore\qquad P=4(r)^t\\\\ -------------------------------\\\\`


`\bf \textit{we also know that } \begin{cases} t=1\\ P=6 \end{cases}\implies 6=4(a)^1\implies \cfrac{6}{4}=a^1 \\\\\\ \cfrac{3}{2}=a\qquad therefore\qquad \boxed{P=4\left((3)/(2) \right)^t}\\\\ -------------------------------\\\\ \textit{now, when t = 3 and t = 4, what is \underline{P}?} \\\\\\ P=4\left((3)/(2) \right)^3\qquad \qquad \qquad P=4\left((3)/(2) \right)^4`