Assume the exponential growth model a(t)equals=upper a 0 e superscript kta0ekt and a world population of 5.95.9 billion in 20062006. if the population must stay below 2424 billion during the next 100 years, what is the maximum acceptable annual rate of growth?

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:

where k is the growth rate, t is time in years and is constant.

The world population is 5.9 billion in 2006.

Thus, t = 0 for 2006

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,

1.4% is the maximum acceptable annual rate of growth such that the population must stay below 24 billion during the next 100 years.

a negative exponent is translated as follows:

so, we have