Question

the population of the world in 1987 was 5 billion and the continuous growth rate was estimated at 2.1% per year. assuming that the world population follows a continuous exponential growth model ( f(t)=ae^{kt} ), find the projected world population 9 years later in 1996. round your answer to 2 decimal places. billion people

Explanation:

Step1: Identify the values of \(a\), \(k\), and \(t\)

Given \(a = 5\) (population in 1987), \(k=0.021\) (growth rate as a decimal), and \(t = 9\) (years from 1987 to 1996).

Step2: Substitute into the formula \(f(t)=ae^{kt}\)

Substitute \(a = 5\), \(k = 0.021\), and \(t=9\) into \(f(t)=ae^{kt}\), we get \(f(9)=5e^{0.021\times9}\).
First calculate \(0.021\times9 = 0.189\). Then \(f(9)=5e^{0.189}\).
Since \(e^{0.189}\approx1.207\) (using a calculator for the exponential function), then \(f(9)=5\times1.207 = 6.035\approx6.04\).

Answer:

\(6.04\)