Now spot the pattern. (555-555*4.5%)=(1-4.5%)555=0.955*555, each year if 4.5% die, then 95.5% survive. So the number alive in 1996 is 0.955*555 and in 1997 is 0.955*(0.955*555) and so on. The short hand way to write this is (0.955^x)*555=number alive x years after 1995.
a.)2010-1995=15 years, so 0.955^15*555=514.8 is the number alive in 2010.
b.) we need to find the x when 0.955^x*555=50,
0.955^x=50/555
log(0.955^x)=log(50/555)
x * log0.955=log(50/555)
x=log(50/555)/log0.955
x=52.275
So 52 years after 1995 the population will have declined to 50, meaning in 1995+52=2047.