Question

In 2000, the world population was estimated to be 6.124 billion people. in 2005, it was 6.515 billion.

a. write an exponential growth equation to represent the population y in billions t years after 2000. round the growth rate to 5 decimal places.

b. use the equation to predict the year the population would reach 7.5 billion people.

Answer 1

To represent the population in billions t years after 2000, we can use the exponential growth equation y = a * (1 + r)^t. By substituting the given population values in 2000 and 2005, we can solve for the growth rate and predict the year the population would reach a certain value.

Step-by-step explanation:

To represent the population in billions t years after 2000, we can use the equation: y = a * (1 + r)t, where y is the population in billions, t is the number of years after 2000, a is the starting population, and r is the growth rate.

Given that the population in 2000 was 6.124 billion, we have the equation: y = 6.124 * (1 + r)t. We can now use the population in 2005 as a reference point. Substituting the values into the equation, we get: 6.515 = 6.124 * (1 + r)5. Solving for r using logarithms, we find that the growth rate is approximately 0.03535.