Arhthie

Consider the polynomial function P(x)=-x3-mx2+nx-5m. The remainder when P(x) is divided by (x-2) is 1 and (x+1) is a factor of P(x). Determine m and n algebraically. Show all your work for full marks.

A culture of bacteria triples every 7 minutes. How long will it take a culture originally consisting of 24 bacteria to grow to a population of 100 000 bacteria? Show ALL work and round to one decimal place, if necessary.