Explanation
We are given the following:
The table above models the function:
[tex]\begin{gathered} f(x)=a(4)^x \\ where \\ a=initial\text{ }value\text{ }(when\text{ }the\text{ }generation)=0 \\ x=generation \end{gathered}[/tex]
We are required to determine how many offspring there would be for the fifth and sixth generations using the equation.
This is achieved thus:
[tex]\begin{gathered} \text{ Offspring:} \\ Fifth\text{ }generation\to a(4)^x \\ where \\ a=6 \\ x=5 \\ F\imaginaryI fth\text{ }generat\imaginaryI on\to6(4)^5=6144 \end{gathered}[/tex][tex]\begin{gathered} Sixth\text{ }generation\to a(4)^x \\ where \\ a=6 \\ x=6 \\ S\imaginaryI xth\text{ }generat\imaginaryI on\to6(4)^6=24576 \end{gathered}[/tex]
Hence, the answers are:
[tex]\begin{gathered} 5th\text{ }generation=6144 \\ 6th\text{ }generation=24576 \end{gathered}[/tex]
