a.) Calculate how many years the population will take to double.
Given:
P = 2Po = 153 008 154 Total Population when doubled
Po = 76 504 077 Original Population
Rate per year
r = 2.36 % or 0.0236
t = ? Years
The formula we are using is..
rt
P = Poe
1

First, plug in the given values to the equation.
rt
P = Poe
153 008 154 = 76 504 077 e(0.0236)t
1
Then reduce both sides by multiplying
76 504 077
( ) ( )
1 1
153 008 154 = 76 504 077 e(0.0236)t
76 504 077 76 504 077
2 = e(0.0236)t
2

Find the ln of both sides. ln e will reduced since it means the same thing.
ln 2 = 0.0236t
1
Isolate t by multiplying
0.0236
)
)
( (
1 1
ln 2 = 0.0236t
0.0236 0.0236
ln 2
= t
0.0236
29.4 years = t
3

b.) Calculate when the population will reach 80 000 000.
Given:
P = 2Po = 153 008 154 Total Population when doubled
Po = 76 504 077 Original Population
Rate per year
r = 2.36 % or 0.0236
t = ? Years
The formula we are using is..
P = Poert
4

First, plug in the given values to the equation.
P = Poert
80 000 000 = 76 504 077 e(0.0236)t
1
Then reduced both sides by multiplying
76 504 077
( )
( ) 1
1 (0.0236)t
80 000 000 = 76 504 077 e 76 504 077
76 504 077
1.045695905 = e(0.0236)t
5

Find the ln of both sides. ln e will reduced since it means the same thing.
ln ( 1.045695905) = 0.0236t
1
Isolate t by multiplying
0.0236
)
) (
( 1
1
ln ( 1.045695905) = 0.0236t
0.0236
0.0236
ln (1.045695905)
= t
(0.0236)
1.9 years = t
6