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.
