This document discusses using exponential and logarithmic equations to model population growth over time. It provides an equation to calculate Jamaica's population P in year y since 2005 based on an original population Po of 2100284 and annual growth rate of 0.95%. Using this equation, it determines that it would take approximately 73 years for Jamaica's population to double, and approximately 38 years to reach 3,000,000 people.

1. EXPONENTS
and
LOGARITHMS

2. In year 2005, the population of
Jamaica was 2100284, and was
increasing at rate of 0.95% per year.

3. Write an equation to represent the population
of Jamaica as a function of number of years, y
since 2005..

4. Population of
Jamaica
P = Po (1+ ) yn
P = 2100284 ( 1 + 0.0095)y
P = 2100284 ( 1.0095)y
Where as: Increasing rate
P - amount of resulting population
Po- principle or original amount
r - percent rate
y - time in years
n – number of times the principle is *Given the equation of
compounded per year population growth, you
just have to plug in the
values

5. For the population of Jamaica to double, how
many years would it take?

6. P = 2100284 ( 1.0095)y
2(2100284) = 2100284 ( 1.0095)y
2 = 1.0095y Use the equation we got
from the first question
ln2 = yln(1.0095)
y = ln(2) *It was stated that the
resulting amount (P)
ln(1.0095) should be doubled, so we
multiply 2 to the original
amount
y 73.3039
*Then we just solve for
(y) – the time in years it
will take to double

7. Calculate when the population will reach
3000000.

8. P = 2100284 ( 1.0095)y
3000000 = 2100284 ( 1.0095)y
3000000 = 2100284 ( 1.0095)y
2100284 2100284
ln (1.4284) = lny(1.0095) *This question is just the
same as the previous one.
y = ln(1.4284)
ln(1.0095) *We just put 3000000 as
the final value instead.
y 37.71