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Sagot :
[tex]8\times4^t[/tex]Explanation:
f(t) = ka^t
[tex]2^{2t+3}is\text{ the same as }2^{\mleft\{2t\mright\}}\times2^3[/tex]Reason: Product of exponents
a^m + a^p = a^(m+p)
when the base is the same and the sign between both base is multiplication, the exponents are added together after picking one of the base
[tex]\begin{gathered} 2^{2t+3}=2^{\{2t\}}\times2^3 \\ =2^{2t}\times8 \end{gathered}[/tex][tex]\begin{gathered} 2^{\{2t\}}=2^{2\times t} \\ =4^t \\ 2^{2t}\times8\text{ }=4^t\times8 \end{gathered}[/tex][tex]\begin{gathered} In\text{ the form:}f\mleft(t\mright)=ka^t \\ 2^{2t+3}=8\times4^t \\ k\text{ = constant= 8} \end{gathered}[/tex]
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