Question

Wk 6
Sec 12.7 #24
World population growth
In 2008 the world population was 6.7 billion and the exponential growth rate was 1.14% per year.
A.Find the exponential growth function
B.Predict the world’s population in 2014
C.When will the world’s population be 8.0 billion?

Could someone help me with this please?

Answer 1

Growth function:
Assume Y=year, so Y=2008 is year 2008, etc.

The exponential growth function is
N(Y)=N(2008)*1.0114^(Y-2008) for Y≥2008
or
N(Y)=(6.7*10^9)*1.0114(Y-2008)
for Y≥2008

Population at 2014 is therefore
N(2014)=(6.7*10^9)*1.0114(2014-2008)
=7.17*10^9

The population will reach 8 billion when
N(Y)=8*10^9
or
(6.7*10^9)*1.0114(Y-2008) = 8*10^9
1.0114(Y-2008)=8/6.7
Take log on each side and solve for Y:
Y-2008=log(8/6.7)/log(1.0114)=15.6 years
So by the middle of 2023, the world population will reach 8 billions.