(a) 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?

(b) A poll commissioned by a politician estimates that t days after he makes a statement denegrating women,the percentage of his constituency (those who support him at the time he made the statement) that still supports him is given by S(t) = 75(t^2 3t + 25) / t^2 + 3t + 25 The election is 10 days after he made the statement.

(i) If the derivative S'(t) may be thought of as an approval rate, derivate the a function for his approval rate.

(ii) When was his support at its lowest level?

(iii) What was his minimum support level?

(iv) Was the approval rate positive or negative on the date of the election?

(c) Lara offers 100 autograph bats. If each is priced at p dollars, it is that the demand curve for the bast will be p = 250 (q/4) . If price elasticity is E(p) = dq/q dp/p . When |E(p)| < 1, demand is inelastic and when |E(p)| > 1, demand is elastic.

(i) Find the price elasticity of demand for Lara s bats.

(ii) Is demand inelastic or elastic?