Q$2).$ Plot the graph of the sequence $\{\frac{2n^3+7}{1+n^3}{\}}_n=1^{20}$ and hence check whether the sequence is monotonic or not.

$(4$ marks$)$

Q$3).$ The number of a certain bacteria organisms $($in billions$)$ produced per second $(t)$ in the body of a wild animal form a sequence given by:

$\{\frac{50t^6-}{3t^{20}-t^3+3}{\}}_t=0^{}$

$($a$)$ Find the number of bacteria that are produced iduring the ${10}^{th}$ second. $(2$ marks$)$

$($b$)$ Assuming that bacteria production continues even after the death of the wild animal, what is the number of bacteria that can produced as $t?(3$ marks$)$