Q$2$f$\_(1)($n$)=$alog$\_(10)($n$)$

f$\_(2)($n$)=$bn$^($c$)$

Where a$,$b are non$-$zero positive constants, and c$>0$ is a real value. A student is

comparing the relative asymptotic running time of these two functions. They can

see that if c$=1$f$\_(2)$ is a linear functionf$\_(2)$ is permanently greater than f$\_(1).$

$($a$)$ If a$=15,$b$=4$ and c$=0\mathrm{.}4,$ for what value of n would f$\_(2)$ permanently exceed

that of f$\_(1)?$ Fill in the blank on the answer sheet.

$[5$ marks$]$

$($b$)$ For values of c$>0,$ but explain whether you think it is possible for the

long$-$term value of f$\_(1)$ to exceed that of f$\_(2).$ Fill in the blanks and check the correct

box on the answer sheet.