We have that the first day, there were 5 bacteria, then on day 2 there were 10, and so on. We can write the table like this:
where 'x' represents the number of days and 'y' represents the total bacteria.
Since we are multiplying by 2 each day the total bacteria, we have a geometric sequence, which can be calculated the nth term like this:
[tex]a_n=a_1r^{n-1}[/tex]in this case, we can write it like this, considering that the number of bacteria on day 1 is 5, and the common ratio is r = 2 :
[tex]y=5\cdot2^{x-1}[/tex]which clearly is not a linear function, but the number of bacteria is afunction of the number of days.
For the days 4 and 5, we can make x = 4 and x = 5 to get the following:
[tex]\begin{gathered} x=4 \\ \Rightarrow y=5\cdot2^{4-1}=5\cdot2^3=5\cdot8=40 \\ x=5 \\ \Rightarrow y=5\cdot2^{5-1}=5\cdot2^4=5\cdot16=80 \end{gathered}[/tex]
