Question

d) Media consultants for the new local magazine IT-Solutions! have projected that the number of subscriptions will grow during the first five years at a rate given by [5 Marks]
S
0
(t) = 1000
(1 + 0.3t)
3/2
, 0 ≤ t ≤ 60
where t is the number of months since the magazine’s first issue and S
0
(t) is the rate of change in the
number of subscriptions measured in subscriptions/month. Evaluate and interpret Z 6
0
S
0
(t) d

Answer 1

Number of subscription per month is given by

S₀(t) = $1000( 1+ 0.3 t )^{3/2}$ for 0 <= t <= 60

= 0 for every other value

Number of subscribers at any time will be given by

$\int 1000(1 + 0.3t)^{3/2} dt$ = $(\frac{4000}{3})((1+0.3t)^{\frac{5}{2}}) + c$

where c is some fix number depending on the number of subscribers in the starting.

Number of subscriber in five years = $\int_{0}^{60} 1000(1 + 0.3t)^{3/2} dt$ = 2096750 (approx)