Applications of Exponential and Logarithmic Functions- Word Problem

Question

The population of the world in 1987 was 5 billion and the relative growth rate was estimated at 2 percent per year. Assuming that the world population follows an exponential growth model, find the projected world population in 1995. Round your answer to 2 decimal places.
Your answer is _____billion people

Answer 1

Let the equation for the population (P) growth be given by

 

P = P₀e^rt, where _P0 is the initial population in billioins at time t,

                            t is the number of years since 1987,

                            r is the rate of growth of population/year

 

_{In this case P0 = 5 billion and r = 0.02.  Putting these values into the equaation:}

 

P = 5e^0.02t

 

Year 1995 is 8 years after 1987, then the population would be

P = 5e^0.02*8 = 5e^0.16 ≈ 5.87 billion people