Question

Please help me with this

Answer 1

`{\Large \begin{array}{llll} y=ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=1\\ y=24 \end{cases}\implies 24=ab^1\implies 24=ab \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=3\\ y=1536 \end{cases}\implies 1536=ab^3\implies 1536=abb^2\implies \stackrel{\textit{substituting from above}}{1536=24b^2} \\\\\\ \cfrac{1536}{24}=b^2\implies 64=b^2\implies √(64)=b\implies \boxed{8=b}`

`\stackrel{\textit{since we know that}}{24=ab}\implies 24=a8\implies \cfrac{24}{8}=a\implies \boxed{3=a} \\\\[-0.35em] ~\dotfill\\\\ {\Large \begin{array}{llll} y=3(8)^x \end{array}} \hspace{15em}\stackrel{\textit{after 6 days}}{y=3(8)^6}\implies y=786432`