Question

Hello I need a little help with my homework. I started trying to work it out but I am not sure if it is the correct solution. Please help!

Question:
Population growth. The exponential growth rate of the population of United Arab Emirates is 4.4% per year (one of the highest in the world). What is the doubling time?

Sources: Based on data from U.S. Census Bureau; International Data Base 2007

My Answer: I changed 4.4% to .044^2. My result was .001936 or round to 0.002%.

Is this correct? Should I be using the P(t) = P0e^kt? If so how should I go by doing so? Thanks for your help in advance!

Answer 1

If the population after year 1 is

P(1)=P(0)x1.044

at the end of year 2 it is

P(2)=P(1)x1.044 = P(0)x1.044^2

at the end of year t it is

P(t)=P(0)x(1.044)^t

to find when population has doubled (i.e. is 2P(0))

2P(0)= P(0)x(1.044)^t

and solve for t


2 = (1.044)^t

log(2)=log(1.044)^t)= txlog(1.044)

thus t=log(2)/log(1.044)

and I got 16.1 years