Solution Let P be the principal at any time t According to the given problem,
dp
dt  =
5
P
⎛100
⎞×
⎜
⎟
⎝
⎠
or
dp
dt  = P
20 (1)
separating the variables in equation (1), we get
P
dp  = 20
dt (2)
Integrating both sides of equation (2), we get
log P =
C1
20
t +
or
P =
C1
et20
e⋅
or
P =
20
C
et
 (where 
C1
C
e
=
)