Five years ago the government of a Pacific Island state launched an extensive propaganda campaign toward curbing the country's population growth

The given population function is P(t) = (-1/3)t³+ 64t+ 300 

so rate of change population can be determined by differentiating the function with respect to t.

initially at t = 0 the population is 300.

now differentiating ,

P'(t) = (-1/3) 3 t² + 64 ( d(xⁿ) / dx = n x^n-1 and d(c) / dx = 0 where c is constant)

P'(t) = -t² + 64 ;

for t = 1 ;

rate of change = P'(1) = -(1)² + 64;

= 63;

for t = 2 ;

rate of change = P'(2) = -(2)² + 64;

= 60;

for t = 3 ;

rate of change = P'(3) = -(3)² + 64;

= 55;

for t = 4 ;

rate of change = P'(4) = -(4)² + 64;

= 48;

Yes, this can be clearly seen the rate of change of population is decreasing so that population is also decreasing, hence this campaign

is a successful propaganda towards curbing the population growth