Question

5, 20, 80, 320, 1,280what recursive function would describe the number of bacteria observed at the nth hour

Answer 1

Notice that the common factor between the terms of the sequence is r = 4, then, a formula for the recursive function is:

`\begin{gathered} a_n=a_1r^(n-1) \\ a_1=5 \\ r=4 \\ \Rightarrow a_n=5\cdot4^(n-1) \end{gathered}`

and the recursive function can be found from this formula:

`\begin{gathered} a_n=a_(n-1)\cdot r \\ \Rightarrow a_n=4a_(n-1) \end{gathered}`