(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?
(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 elasticily 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
s bats. [5 mks]
(ii) Is demand inelastic or elastic?
Hello. Since you have posted multiple questions and not specified which question needs to be solved, we will solve the first question for you. If you want any other specific question to be solved, then please resubmit only that question or specify that part only.
a.i)
According to the question the sales function is given as
S = 300000(1-e -0.06t)
For the proof of the function will never attain the maximum value we have to maximize the sales function.
d(s)/dt = 18000
Second-order differentiation will be zero so, we can say it will never attain the maxima
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