Answer:
1.4% is the maximum acceptable annual rate of​ growth such that the population must stay below 24 billion during the next 100​ years.
Step-by-step explanation:
We are given the following in the question:
The exponential growth model ​is given by:
[tex]A(t) = A_0e^{kt}[/tex]
where k is the growth rate, t is time in years and [tex]A_0[/tex] is constant.
The world population is 5.9 billion in 2006.
Thus, t = 0 for 2006
[tex]A_0 = 5.9\text{ billions}[/tex]
We have to find the maximum acceptable annual rate of​ growth such that the population must stay below 24 billion during the next 100​ years.
Putting these values in the growth model, we have,
[tex]24 = 5.9e^{100k}\\\\k = \dfrac{1}{100}\ln \bigg(\dfrac{24}{5.9}\bigg)\\\\k = 0.01403\\k = 0.01403\times 100\% = 1.4\%[/tex]
1.4% is the maximum acceptable annual rate of​ growth such that the population must stay below 24 billion during the next 100​ years.
