the population of a town grows uniformly at a rate of 4% every year in how many years will the population of town grows from 1562000 to 1757 600
Step wise explanation
Answers
ANSWER
Since increase in population speeds up with increase in population and let x be the population at any time t
∴
dt
dx
α x
dt
dx
=rx
where r is proportionality constant.
Rewriting,
x
dx
=rdt
Integrating,
lnx=rt+c
where c is the a constant
Exponentiating on both sides with e
x=e
rt+c
=Ae
rt
, where A=e
c
Let the initial population x
0
, then
x
0
=A…(1)
If the population is increased 4 times in time t, then
4x
0
=Ae
rt
…(2)
From (1), x=A
4x
0
=x
0
e
rt
Taking log on both sides
ln4=rt
r=0.1...(as rate of increase is given as 10%)
t=
0.1
ln4
=
0.1
1.38
=13.8 years that is 13 years and around 10 months
Answer:
Since increase in population speeds up with increase in population and let x be the population at any time t
∴
dt
dx
α x
dt
dx
=rx
where r is proportionality constant.
Rewriting,
x
dx
=rdt
Integrating,
lnx=rt+c
where c is the a constant
Exponentiating on both sides with e
x=e
rt+c
=Ae
rt
, where A=e
c
Let the initial population x
0
, then
x
0
=A…(1)
If the population is increased 4 times in time t, then
4x
0
=Ae
rt
…(2)
From (1), x=A
4x
0
=x
0
e
rt
Taking log on both sides
ln4=rt
r=0.1...(as rate of increase is given as 10%)
t=
0.1
ln4
=
0.1
1.38
=13.8 years that is 13 years and around 10 months
Step-by-step explanation: