JKUAT DEPARTMENT OF STACS
STA 2490 DEMOGRAPHIC TECHNIQUES
B Sc Actuarial Science/Biostatistics/Statistics Assignment
Hand in on 13 February 2015
1. The logistic population model satisfies the differential equation
dP
 k P  A  P  where
dt
P is the population at time t, and k and a are positive constants.
(i)
By differentiating the given differential equation with respect to t, show that
A
thegraph of P against t has a point of inflexion when P  .
2
A
(ii)
By integrating the differential equation, given that P  at t  0, show that P
4
A
.
and t are related by the equation P 
1  3e  Ak t
(iii)
Show that the point of inflexion on the graph of P against t occurs when t 
n 3
.
Ak
JKUAT DEPARTMENT OF STACS
STA 2490 DEMOGRAPHIC TECHNIQUES
B Sc Actuarial Science/Biostatistics/Statistics Assignment
Hand in on 13 February 2015
2. The logistic population model satisfies the differential equation
dP
 k P  A  P  where
dt
P is the population at time t, and k and a are positive constants.
(iv)
By differentiating the given differential equation with respect to t, show that
A
thegraph of P against t has a point of inflexion when P  .
2
A
(v)
By integrating the differential equation, given that P  at t  0, show that P
4
A
.
and t are related by the equation P 
1  3e  Ak t
(vi)
Show that the point of inflexion on the graph of P against t occurs when t 
n 3
.
Ak