Question

According to this model the world population will be 9 billion in? Round to the nearest whole number as needed

Answer 1

A logistic growth model for the world population is:

`f(x)=(12.57)/(1+4.11\cdot e^(-0.026x))`

Where x is the number of years since 1958 and f(x) is expressed in billions

It's required to find the year for which the world population will be f(x) = 9 billion.

Then we set up the equation:

`9=(12.57)/(1+4.11\cdot e^(-0.026x))`

Cross-multiplying:

`9(1+4.11\cdot e^(-0.026x))=12.57`

Dividing by 9:

`1+4.11\cdot e^(-0.026x)=1.3967`

Subtracting 1 and dividing by 4.11:

`\begin{gathered} 4.11\cdot e^(-0.026x)=1.3967-1=0.3967 \\ e^(-0.026x)=0.0965126 \end{gathered}`

Taking logarithms on both sides:

`\begin{gathered} -0.026x=\log0.0965126 \\ Dividing\text{ by -0.026:} \\ x=(\log0.0965126)/(-0.026) \\ x=90 \end{gathered}`

According to this model, the world population will be 9 billion in 90 years from 1958, that is, in the year 2048