The sales of a book publication are expected to grow according to the function S = XXXXXXXXXX − e− 0.06t ),where t is the time, given in days. (i) Show using differentiation that the sales never...

  The sales of a book publication are expected to grow according to the function
S = 300000(1 − e−^0.06t),where t is the time, given in days.

(i) Show using differentiation that the sales never attains an exact maximum value.
(ii) What is the limiting value approached by the sales function?

A town has a population of 5000 persons, but is expected to grow by 2% every year.
(i) What would be the population size in 7 years?

(ii) Find the sum of the first eight terms of the sequence  1/8, -1/4,  1/2..