the population of the world in 1987 was 5 billion and the continuous growth rate was estimated at 2.1% per…

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

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

Answer

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)